You need to learn your church history.
Ignatius
Ignatius died in 110 AD. He was a disciple of the Apostle John and was the bishop of Antioch. He was martyred in Rome only 10 years after John died. Ignatius is as close to the source as you can get. He had several interesting quotes concerning the Trinity doctrine:
"Be deaf, therefore, when any would speak to you apart from Jesus Christ, who was descended from the family of David, born of Mary, who truly was born, truly took a body; for the Word became flesh and dwelt among us without sin"
Ignatius also wrote about Jesus’ second coming:
“Look for him that is above the times, him who has not times, him who is invisible”.
He believed that only God is was timeless and in his letter to Polycarp, Ignatius stated, “Jesus is God, God incarnate.”
Ignatius also identified Jesus apart from the Father and the Holy Spirit by saying,
“In Christ Jesus our Lord, by whom and with whom be glory and power to the Father with the Holy Spirit for ever”.
He also believed Jesus was fully God and fully man. He clarified this by saying,
“We have also as a Physician the Lord our God Jesus the Christ the only-begotten Son and Word, before time began, but who afterwards became also man, of Mary the virgin. For ‘the Word was made flesh.' Being incorporeal, He was in the body; being impassible, He was in a passible body; being immortal, He was in a mortal body; being life, He became subject to corruption, that He might free our souls from death and corruption, and heal them, and might restore them to health, when they were diseased with ungodliness and wicked lusts.” ( The ante-nicene Fathers, Grand Rapids: Eerdmans, Vol. 1, p. 52 .)
He clarifies this further in one of his epistles to the church in Ephesus:
“...God Himself appearing in the form of a man, for the renewal of eternal life.”( Epistle of Ignatius to the Ephesians 4:13)
Also in this epistle, Ignatius again identifies Jesus as God while identifying His personhood:
“For our God Jesus Christ, was, according to the appointment of God, conceived in the womb by Mary, of the seed of David, but by the Holy Ghost.” ( Epistle of Ignatius to the Ephesians 4:9)
In his letter to the Trallians, Ignatius refers to Jesus as God and being distinguished from the Father:
( Epistle of Ignatius to the Trallians 2:4)
"For even our God, Jesus Christ, now that He is in the Father".
These writings are over 200 years before the Council of Nicaea. He wrote during and very shortly after the life of the Apostle John who was called the beloved of Jesus.
Justin the Martyr
Around 130 AD, Justin explained Christian baptism:
“For, in the name of God, the Father and Lord of the universe, and of our Savior Jesus Christ, and of the Holy Spirit, they then receive the washing with water”
Polycarp
Polycarp lived to be 90 years old. He was martyred in 160 AD. He was also a disciple of the Apostle John and the bishop of Smyrna. His doctrine about Jesus was also directly from the source. Polycarp also makes a clear distinction between Jesus, the Father and the Holy Spirit:
“O Lord God almighty...I bless you and glorify you through the eternal and heavenly high priest Jesus Christ, your beloved Son, through whom be glory to you, with Him and the Holy Spirit, both now and forever”
In Polycarp’s epistle to the church at Philippi, he identifies the Father as God, Jesus as the eternal High Priest and God and also distinguishes between the personhood of the Father and the Son:
“Now may the God and Father of our Lord Jesus Christ, and the eternal High Priest Himself, the God Jesus Christ, build you up in the faith...”( The Epistle of Polycarp to the Church at Philippi, 12
Iranaeus
Iranaeus was influenced by Polycarp and later became the bishop of Lyons. 145 years before the Council of Nicaea, Iranaeus confronted the growing heresy in the church. In his work, ‘Iranaeus Against Heresy’, he confronts the notion that Jesus was a man and not God in the flesh. He wrote:
“But he Jesus is himself in his own right, beyond all men who ever lived, God, Lord, and king eternal, and the incarnate word, proclaimed by all the prophets, the apostles …The Scriptures would not have borne witness to these things concerning Him, if, like everyone else, He were mere man.” (Against Heresies 3:19.1-2)
Iranaeus then went on to explain that Jesus is the Word and the Father created all things through Him while affirming the plurality of the Godhead:
"For with Him were always present the Word and Wisdom, the Son and the Spirit, by whom and in whom, freely and spontaneously, He made all things, to whom also He speaks, saying, 'Let us make man after our image and likeness'".( Against Heresies, 4:10)
Don’t miss the important focal point here. Iranaeus was confronting the heresy that the Gnostics and other groups were trying to marry to Christian doctrine. He was confronting a new doctrine the church stood against, he was not introducing new doctrine.
Iranaeus then went on to present a clear belief in the Triune God:
"The Church, though dispersed throughout the whole world, even to the ends of the earth, has received from the apostles and their disciples this faith: ...one God, the Father Almighty, Maker of heaven, and earth, and the sea, and all things that are in them; and in one Christ Jesus, the Son of God, who became incarnate for our salvation; and in the Holy Spirit, who proclaimed through the prophets the dispensations of God, and the advents, and the birth from a virgin, and the passion, and the resurrection from the dead, and the ascension into heaven in the flesh of the beloved Christ Jesus, our Lord, and His manifestation from heaven in the glory of the Father ‘to gather all things in one,' and to raise up anew all flesh of the whole human race, in order that to Christ Jesus, our Lord, and God, and Savior, and King, according to the will of the invisible Father, ‘every knee should bow, of things in heaven, and things in earth, and things under the earth, and that every tongue should confess; to him, and that He should execute just judgment towards all...'" (Against Heresies X.l)
Theophilus
Theophilus was the bishop of Antioch and is identified in Luke 1:3 and Acts 1:1. He sent this in a letter to Autolycus in 160 AD (165 years before the Council of Nicaea):
For the divine writing itself teaches us that Adam said that he had heard the voice but what else is this voice but the word of God, who is also his Son.
Tertullian
Tertullian was a respected apologist wrote much in defense of Christianity. Around 200 AD he wrote:
“The origins of both his substances display him as man and as God: from the one, born, and from the other, not born” (The Flesh of Christ 5:6-7).
“God alone is without sin. The only man without sin is Christ; for Christ is also God.”(The Soul 41.3)
He was a defender of Christianity. He was addressing attacks against the church, which questioned the deity of Christ. Critics accuse the church of changing the message, but as we see from history, the church was defending Christianity from those attempting to change it.
Tertullian contended against Praxeas concerning the new doctrine we now call Modalism. Praxeas took his beliefs from Sabellius. This view of Modalism teaches that there is one in the Godhead and He takes different forms: the Father = the Son = the Holy Spirit. They are different modes of the same God. Sabellius refined his doctrine around the beginning of the third century. He explained his belief:
"the existence of a divine monad (which he named the huiopater) which by a process of expansion projected itself successively in revelation as the Father, Son, Holy Spirit. So each appeared in different periods of time, instead of existing simultaneously. The Father was the creator and law giver, the Son was the redeemer and the Holy Spirit was the giver of grace and the regenerator."
Epiphanius, bishop of Salamis wrote in 375 in his volume about heresies,
“Their doctrine is, that Father, Son and Holy Spirit are one and the same being, in the sense that three names are attached to the one substance. A close analogy may be found in the body, soul and spirit of man.”
This is similar to the ‘modes’ of God claimed by Oneness Pentecostals today.
This was never accepted by the church and was considered heresy. Tertullian argued against this by stating the church’s historic belief that,
“We define that there are two, the Father and the Son, and three with the Holy Spirit, and this number is made by the pattern of salvation...[which] brings about unity in trinity, interrelating the three, the Father, the Son, and the Holy Spirit. They are of one substance and power, because there is one God from whom these degrees, forms and kinds devolve in the name of Father, Son and Holy Spirit.” (Against Praxeas p. 156-7).
“The connection of the Father in the Son the Son in the paraclete (Holy Spirit), produces three coherent persons, who are yet distinct one from another. These three are one essence, not one person, as it is said, ‘I and my Father are one,’ in respect of unity of substance, not singularity of number.”… “Yet we have never given vent to the phrases ‘two Gods’, or ‘two Lords’: not that it is untrue the Father is God, the Son is God, the Spirit is God, each is God.” ( Ante-Nicene fathers vol.3,p.621, Against Praxeas.)
Tertullian ads to this definition by saying:
“We believe there is but one God, and no other besides the maker of the world, who produced the universe out of nothing, by his word sent forth first of all, that this word, called his Son, was seen in the name of God in various ways by the patriarchs, was always heard in the prophets, at last sent down, from the spirit and power of God the Father, into the virgin Mary, was made flesh in her womb, and born of her, lived as Jesus Christ...”
Hippolytus
Hippolytus was appointed Bishop in Rome by his followers when he seceded from the church in protest of Zephyrinus being appointed as Bishop. He opposed Zephyrinus because he taught modalist views. Hippolytus also opposed Zephyrinus’ views on penance and absolution – the belief that the earthly bishop could declare forgiveness of post-baptism sins. During persecution, Hippolytus was sent to the mines with the new Bishop of Rome, Pontain who did not hold to these views. Hippolytus reconciled himself with the church and urged his followers to do so as well. Both bishops resigned to end the division and to allow a new bishop to succeed them. Hippolytus and Pontain were martyred together. Hippolytus wrote the following in the ‘Apostolic Tradition’ around 200 AD:
“1. Do you believe in God, the Father Almighty? 2. Do you believe in Christ Jesus, the Son of God, who was born by the Holy Spirit of the Virgin Mary, and was crucified under Pontius Pilate, and was dead and buried, and rose again the third day, alive from the dead, and ascended into heaven, and sat at the right hand of the Father, and will come to judge the living and the dead? 3. Do you believe in the Holy Spirit, in the holy church, and in the resurrection of the flesh?”
Ten years earlier, Hippolytus wrote against the heresy of Noetus. Noetus taught what is now known as Oneness doctrine. He believed that the Father = the Son = the Holy Spirit. In response, Hippolytus wrote:
John 1:1 In the beginning was the Word, and the Word was with God, and the Word was God.
“If then the word was with God and was also God what follows? Would one say that he speaks of two God’s? I shall not speak of two Gods but of one; of two persons however and of a third economy, the grace of the Holy Ghost. For the Father is indeed one but there are two persons because there is also the son; and there is the third the Holy Spirit. The Father decrees, the word executes and the son is manifested, through whom the Father is believed on. The economy of the harmony is led back to the one God, for God is one. It is the father who commands and the son who obeys and the Holy Spirit who gives understanding; The Father is above all the son is through all and the Holy Spirit who is in all. And we cannot think of one God, but by believing in truth in Father and Son and Holy Spirit”.
Hippolytus also wrote:
“God, subsisting alone, and having nothing contemporaneous with Himself, determined to create the world....Beside Him there was nothing; but He, while existing alone, yet existed in plurality....And thus there appeared another beside Himself. But when I say another, I do not mean that there are two Gods....Thus, then, these too, though they wish it not, fall in with the truth, and admit that one God made all things....For Christ is the God above all.....He who is over all is God; for thus He speaks boldly, 'All things are delivered unto me of my Father.' He who is over all, God blessed, has been born; and having been made man, He is (yet) God for ever....And well has he named Christ the Almighty.” (Hippolytus " The Ante-Nicene Fathers, vol. 5, pp. 227, 153, 225)
Athanasius
Athanasius challenged Arius’ heresy on the non-deity of Christ. Arius was the primary reason the council of Nicaea was called. Arius challenged the deity of Christ by claiming that Jesus did not pre-exist. Arius claimed that Jesus was created for the purpose of being incarnated and was not God. Athanasius challenged Arius and a bitter dispute arose when Arius began a letter campaign to get leaders to side with him. He also created jingles and taught his heresy through music. In defense of historic Christianity, Athanasius wrote:
“[The Trinity] is a Trinity not merely in name or in a figurative manner of speaking; rather, it is a Trinity in truth and in actual existence. Just as the Father is he that is, so also his Word is one that is and is God over all. And neither is the Holy Spirit nonexistent but actually exists and has true being.” (Letters to Serapion 1:28).
http://www.exchangedlife.com/Sermons/topical/trinity/church_believed.shtml
There are cult groups (Jehovah's Witnesses, The Way International, Christadelphians, etc.) who deny the Trinity and state that the doctrine was not mentioned until the 4th Century until after the time of the Council of Nicea (325). This council "was called by Emperor Constantine to deal with the error of Arianism [see page 45] which was threatening the unity of the Christian Church."
The following quotes show that the doctrine of the Trinity was indeed alive-and-well before the Council of Nicea:
Polycarp (70-155/160). Bishop of Smyrna. Disciple of John the Apostle.
"O Lord God almighty... I bless you and glorify you through the eternal and heavenly high priest Jesus Christ, your beloved Son, through whom be glory to you, with Him and the Holy Spirit, both now and forever" (n. 14, ed. Funk; PG 5.1040).
Justin Martyr (100?-165?). He was a Christian apologist and martyr.
"For, in the name of God, the Father and Lord of the universe, and of our Savior Jesus Christ, and of the Holy Spirit, they then receive the washing with water" (First Apol., LXI).
Ignatius of Antioch (died 98/117). Bishop of Antioch. He wrote much in defense of Christianity.
"In Christ Jesus our Lord, by whom and with whom be glory and power to the Father with the Holy Spirit for ever" (n. 7; PG 5.988).
"We have also as a Physician the Lord our God Jesus the Christ the only-begotten Son and Word, before time began, but who afterwards became also man, of Mary the virgin. For ‘the Word was made flesh.' Being incorporeal, He was in the body; being impassible, He was in a passable body; being immortal, He was in a mortal body; being life, He became subject to corruption, that He might free our souls from death and corruption, and heal them, and might restore them to health, when they were diseased with ungodliness and wicked lusts." (Alexander Roberts and James Donaldson, eds., The ante-Nicene Fathers, Grand Rapids: Eerdmans, 1975 rpt., Vol. 1, p. 52, Ephesians 7.)
Irenaeus (115-190). As a boy he listened to Polycarp, the disciple of John. He became Bishop of Lyons.
"The Church, though dispersed throughout the whole world, even to the ends of the earth, has received from the apostles and their disciples this faith: ...one God, the Father Almighty, Maker of heaven, and earth, and the sea, and all things that are in them; and in one Christ Jesus, the Son of God, who became incarnate for our salvation; and in the Holy Spirit, who proclaimed through the prophets the dispensations of God, and the advents, and the birth from a virgin, and the passion, and the resurrection from the dead, and the ascension into heaven in the flesh of the beloved Christ Jesus, our Lord, and His manifestation from heaven in the glory of the Father ‘to gather all things in one,' and to raise up anew all flesh of the whole human race, in order that to Christ Jesus, our Lord, and God, and Savior, and King, according to the will of the invisible Father, ‘every knee should bow, of things in heaven, and things in earth, and things under the earth, and that every tongue should confess; to him, and that He should execute just judgment towards all...'" (Against Heresies X.l)
Tertullian (160-215). African apologist and theologian. He wrote much in defense of Christianity.
"We define that there are two, the Father and the Son, and three with the Holy Spirit, and this number is made by the pattern of salvation... [which] brings about unity in trinity, interrelating the three, the Father, the Son, and the Holy Spirit. They are three, not in dignity, but in degree, not in substance but in form, not in power but in kind. They are of one substance and power, because there is one God from whom these degrees, forms and kinds devolve in the name of Father, Son and Holy Spirit." (Adv. Prax. 23; PL 2.156-7).
Origen (185-254). Alexandrian theologian. Defended Christianity and wrote much about Christianity.
"If anyone would say that the Word of God or the Wisdom of God had a beginning, let him beware lest he direct his impiety rather against the unbegotten Father, since he denies that he was always Father, and that he has always begotten the Word, and that he always had wisdom in all previous times or ages or whatever can be imagined in priority... There can be no more ancient title of almighty God than that of Father, and it is through the Son that he is Father" (De Princ. 1.2.; PG 11.132).
"For if [the Holy Spirit were not eternally as He is, and had received knowledge at some time and then became the Holy Spirit] this were the case, the Holy Spirit would never be reckoned in the unity of the Trinity, i.e., along with the unchangeable Father and His Son, unless He had always been the Holy Spirit." (Alexander Roberts and James Donaldson, eds., The Ante-Nicene Fathers, Grand Rapids: Eerdmans, 1975 rpt., Vol. 4, p. 253, de Principiis, 1.111.4)
"Moreover, nothing in the Trinity can be called greater or less, since the fountain of divinity alone contains all things by His word and reason, and by the Spirit of His mouth sanctifies all things which are worthy of sanctification..." (Roberts and Donaldson, Ante-Nicene Fathers, Vol. 4, p. 255, de Principii., I. iii. 7).
If, as the anti-Trinitarians maintain, the Trinity is not a biblical doctrine and was never taught until the council of Nicea in 325, then why do these quotes exist? The answer is simple: the Trinity is a biblical doctrine and it was taught before the council of Nicea in 325 A.D.
Part of the reason that the Trinity doctrine was not "officially" taught until the time of the Council of Nicea is because Christianity was illegal until shortly before the council. It wasn't really possible for official Christian groups to meet and discuss doctrine. For the most part, they were fearful of making public pronouncements concerning their faith.
Additionally, if a group had attacked the person of Adam, the early church would have responded with an official doctrine of who Adam was. As it was, the person of Christ was attacked. When the Church defended the deity of Christ, the doctrine of the Trinity was further defined.
The early church believed in the Trinity, as is evidenced by the quotes above, and it wasn't necessary to really make them official. It wasn't until errors started to creep in that councils began to meet to discuss the Trinity, as well as other doctrines that came under fire.