As a matter of fact, God does not save through covenant.
What we call Christianity is directly tied to the Mosaic and Abraham Covenants. Redemptive history is recorded in the bible from Genesis to Revelation and is historical fact whether you want to believe this or not.
25 Then he said unto them,
O fools, and slow of heart to believe all that the prophets have spoken:
26
Ought not Christ to have suffered these things, and to enter into his glory?
27
And beginning at Moses and all the prophets, he expounded unto them in all the scriptures the things concerning himself. Luke 24:25–27.
A covenant implies that God does something for men in exchange of something men do for God.
Not necessarily true. There is no requirement of faith in the Abraham and Mosaic Covenants except that in the Abraham Covenant God requires circumcision, and the Mosaic Covenant God requires obedience to His Law. The New Covenant prophesied by Jeremiah in his writings (31:31-34) is only the Mosaic Covenant fulfilled by Jesus Christ as described at the last Passover meal with Jesus and His twelve disciples for the purpose of establishing the means of the salvation of those chosen by God from [before] the foundation (creation) of the world (Rev. 13: 8.)
The Abrahamic Covenant: (Circumcision)
10 This is my covenant, which ye shall keep, between me and you and thy seed after thee; Every man child among you shall be circumcised.
11 And
ye shall circumcise the flesh of your foreskin; and it shall be a token of the covenant betwixt me and you.
Genesis 17:10–11.
The Mosaic Covenant: (Obedience)
5
Now therefore, if ye will obey my voice indeed, and keep my covenant, then ye shall be a peculiar treasure unto me above all people: for all the earth is mine:
6 And ye shall be unto me a kingdom of priests, and an holy nation. These are the words which thou shalt speak unto the children of Israel. Exodus 19:5–6.
In the
New Covenant established by the blood (life) of Jesus of Nazareth on the night He died, God does not require anything of the Hebrew people (House of Israel and House of Judah.)
27 And he took the cup, and gave thanks, and gave it to them, saying,
Drink ye all of it;
28
For this is my blood of the new testament, which is shed for many for the remission of sins. Mt 26:27–28.
33 But
this shall be the covenant that I will make with the house of Israel;
After those days, saith the LORD,
I will put my law in their inward parts,
And write it in their hearts;
And will be their God,
And they shall be my people.
Jeremiah 31:33.
It implies a symmetrical right between God and men to place demands in each other.
That might be Websters definition, but God is not bound by men's definition and establishes His own definition of things concerning His creation.
9 Remember the former things of old:
For I am God, and there is none else;
I am God, and there is none like me,
10 Declaring the end from the beginning,
And from ancient times the things that are not yet done,
Saying,
My counsel shall stand,
And I will do all my pleasure:
Isiah 46:9–10.
Covenants are a tool, a metaphor used by God so that ancient people could understand their relationship as a relationship between a Ruler and his subjects.
Covenant promises by God may be a tool to accomplish a purpose or goal, but it is not a metaphor since the promises of God to Abram the Hebrew and his Hebrew seed is actual and has been shown throughout Scripture and history as promises that have been fulfilled and will be fulfilled as time moves forward towards their prophetic end.
19 God is not a man, that he should lie;
Neither the son of man, that he should repent:
Hath he said, and shall he not do it?
Or hath he spoken, and shall he not make it good?
20 Behold, I have received commandment to bless: and he hath blessed;
And I cannot reverse it.
21
He hath not beheld iniquity in Jacob,
Neither hath he seen perverseness in Israel:
The LORD his God is with him,
And the shout of a king is among them.
Numbers 23:19–21.
But in reality, God’s salvation is not something man can demand based on what man does, or speaks, or thinks, or believes.
God is not legally obliged before man.
God's obligation towards the Hebrew people is directly tied to His promises to this people. There is extensive evidence in the Hebrew Scripture that describes the character of God and the natural character of man both in covenant and without covenant. In the universe God created it is His prerogative as to what He will do or not do with His creation.
20 Nay but, O man, who art thou that repliest against God?
Shall the thing formed say to him that formed it, Why hast thou made me thus?
21
Hath not the potter power over the clay, of the same lump to make one vessel unto honour, and another unto dishonour?
22 What if God, willing to shew his wrath, and to make his power known, endured with much longsuffering the vessels of wrath fitted to destruction:
23 And that he might make known the riches of his glory on the vessels of mercy,
which he had afore prepared unto glory, Romans 9:20–23.
Therefore, God does not save through covenant.
26
And so all Israel shall be saved: as it is written,
There shall come out of Sion the Deliverer, and shall turn away ungodliness from Jacob:
27
For this is my covenant unto them, when I shall take away their sins. Romans 11:26–27.
God teaches through covenants, as a didactic method, just as He teaches through many other means and metaphors… for example, blood atonement, baptism, resurrection, heaven, hell, names, etc.
16
All [Hebrew] scripture is given by inspiration of God, and is profitable for doctrine,
for
reproof,
for
correction,
for
instruction in righteousness:
17
That the man of God may be perfect, throughly furnished unto all good works.
2 Ti 3:15–17.
God saves everyone who truly and humbly believes can be saved.
As the passage below declares: God has covenant with the Hebrew people and the Hebrew people through the personal sacrifice of the Son of God for sin are saved being the beneficiaries of that covenant and its promises and shall be saved by virtue of said covenant.
4 But when the fulness of the time was come, God sent forth his Son, made of a woman,
made under the law,
5
To redeem them that were under the law, that we might receive the adoption of sons. Galatians 4:4–5.