The New Covenant is the mechanism of delivery for the Gospel, which God preached beforehand to Abraham, “In you all the families of the earth shall be blessed” (Gen 12:3b; Gal 3:8).
Salvation is accorded to New Covenant participants who believe (Gen 15:6), and those individuals are described as the “sons of Abraham,” and comprise the many nations to whom Abraham is father.
The common features of God’s covenant/words/promise(s) to Abraham in Genesis 12, 15, and 17 are that God will bless, God will multiply, and God will give the land, also that this will all be done through Abraham and his offspring.
Circumcision is the sign of the covenant between God and Abraham and was the sign feature of Abraham and his descendants “keeping” their obligation in this covenant relationship. “This is my covenant, which you shall keep, between me and you and your offspring after you: Every male among you shall be circumcised” (Gen 17:10). The problem, of course, is that Abraham’s descendants don’t keep their side of the bargain; they neither walk blamelessly before God nor circumcise every male on the eighth day.
So long as this covenant depends on the actions of the human participants it is the Old Covenant (“All the words that the LORD has spoken we will do.” Ex. 24:3 “All that the LORD has spoken we will do and we will hear/obey” Ex. 24:7 “circumcise your hearts” Dt 10:16) The key, however, is that God is going to keep the covenant, as is foretold in Deuteronomy, where before the book ends God has promised, “the LORD your God will circumcise your heart and the heart of your offspring, so that you will love the LORD your God with all your heart and with all your soul, that you may live” (Dt. 30:6).
As Jeremiah makes clear, the promise of the New Covenant is that God is going to circumcise their hearts, aka, “write [the law] on their hearts… for I will forgive their iniquity and remember their sins no more” (Jer. 31:31-34). These are obvious descriptions of the details of the Gospel promise(s).
So, while circumcision is the sign of the Old Covenant (“which you shall keep”), baptism becomes the sign of the circumcision of the heart. That sign—as is fitting of a superior covenant (Heb. 7:19, 22)—is applied not just to the men, but to every participant in the family of those descended from Abraham by faith.
In the same way as circumcision was given to all who were a part of the Old Covenant family, but it did not impart salvation, so the New Covenant sign is applied to all born into the New Covenant family, though the sign does not impart salvation.
How, someone might ask, do we know that baptism is the sign of the New Covenant?
First, because it is a sign of a spiritual act: the circumcision of the heart, rather than a physical act executed upon the old man. Second, because Paul states that we have been “buried with [Christ] by baptism into death so that we too might walk in newness of life (Romans 6:3-4). Third, because Peter writes that “baptism… now saves you, not as a removal of dirt from the body but as an appeal to God for a good conscience, through the resurrection of Jesus Christ” (1 Peter 3:21). Finally, because Paul tells us that “the circumcision of Jesus Christ is having been buried with him in baptism, in which you were also raised with him through faith,” which takes us right back to Abraham, who was credited righteousness because of faith, and whose descendants are those who believe—those “of faith.”
The inescapable conclusion is that baptism is the sign of New Covenant identification, which like the Old Covenant sign, is given both to new converts and the offspring of covenant participants. Like the Old Covenant sign, the New Covenant sign does not itself save but signifies the saving work of God through Christ.