Jesus told Nicodemus that we MUST be born again, in order to see and enter the Kingdom of God. We also know that entry to the Kingdom of God is through faith in Jesus Christ, which means that being born again precedes (at least in logical order) faith in Jesus Christ.
The Bible is also clear that eternal life is given after we have faith in Jesus Christ, which means that being born again and being given eternal life are different things.
To enter yes
The issue here however is the relation of faith and the new birth
New life (regeneration) is the new birth
Regeneration by definition is the impartation of life
The following verses show faith precedes life
John 5:24 (KJV) Verily, verily, I say unto you, He that heareth my word, and believeth on him that sent me, hath everlasting life, and shall not come into condemnation; but is passed from death unto life.
John 5:25 Verily, verily, I say unto you, The hour is coming, and now is, when the dead shall hear the voice of the Son of God: and they that hear shall live.
John 20:31 (KJV)
31 But these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name.
John 5:40 (KJV)
40 And ye will not come to me, that ye might have life. (one comes to Jesus by faith)
Acts 11:18 (KJV)
18 When they heard these things, they held their peace, and glorified God, saying, Then hath God also to the Gentiles granted repentance unto life.
Regeneration makes one a child of God. Born of God -
One is made a child of God through faith
John 1:12 (KJV)
12 But as many as received him, to them gave he power to become the sons of God,
even to them that believe on his name:
Galatians 3:26 (KJV)
26 For ye are all the children of God by faith in Christ Jesus.
John 12:36 (KJV)
36 While ye have light, believe in the light, that ye may be the children of light. These things spake Jesus, and departed, and did hide himself from them.
Regeneration is a spiritual resurrection. (all agree quickening - being made alive speaks of regeneration when spoken of the physically living)
We are raised spiritually through faith
Colossians 2:12 (KJV)
12 Buried with him in baptism, wherein also ye are risen with
him through the faith of the operation of God, who hath raised him from the dead.
One is born again(regenerated) through faith in gospel
James 1:18 (KJV)
18 Of his own will begat he us with the word of truth, that we should be a kind of firstfruits of his creatures.
1 Peter 1:23 (KJV)
23 Being born again, not of corruptible seed, but of incorruptible, by the word of God, which liveth and abideth for ever.
1 Corinthians 4:15 (KJV)
15 For though ye have ten thousand instructors in Christ, yet
have ye not many fathers: for in Christ Jesus I have begotten you through the gospel.
Of course unbelief does not profit so it must be through faith
Hebrews 4:2 (KJV 1900) — 2 For unto us was the gospel preached, as well as unto them: but the word preached did not profit them, not being mixed with faith in them that heard it.
Regeneration is the mechanism of salvation
Titus 3:5 (KJV)
5 Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost;
Ephesians 2:5 (KJV)
5 Even when we were dead in sins, hath quickened us together with Christ, (by grace ye are saved
it is through faith we are saved
EPH 2:8 (KJV)
Ephesians 2:8 For by grace are ye saved
through faith; and that not of yourselves: it is the gift of God:
.through - dia instrument or means in the genitive case - Vines
Regeneration is preceded by remission of sin
Colossians 2:13 (KJV)
13 And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him
, having forgiven you all trespasses;
God regenerates those he has forgiven
foregiveness requires both faith and repentance
Acts 10:43 (KJV)
43 To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins.