This is to serve as a brief overview providing biblical support for why God has said to initiate our children into the covenant with baptism. Starting with Galatians 3:
Gal 3:29 “And if you are Christ’s, then you are Abraham’s offspring, heirs according to promise.”
Believers are considered children of Abraham because we have faith in Jesus. Not because of our ethnicity. Therefore we look to the sign of the Abrahamic Covenant:
Gen 17:9 And God said to Abraham, “As for you, you shall keep my covenant, you and your offspring after you throughout their generations.
Gen 17:10 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 17:11 You shall be circumcised in the flesh of your foreskins, and it shall be a sign of the covenant between me and you.
Gen 17:12 He who is eight days old among you shall be circumcised. Every male throughout your generations, whether born in your house or bought with your money from any foreigner who is not of your offspring,
Gen 17:13 both he who is born in your house and he who is bought with your money, shall surely be circumcised. So shall my covenant be in your flesh an everlasting covenant.
Gen 17:14 Any uncircumcised male who is not circumcised in the flesh of his foreskin shall be cut off from his people; he has broken my covenant.”
Clearly children were considered part of the Abrahamic covenant not by having faith but by birth. They were recognized as being in the covenant because their parents were. Being members of the covenant they were to receive the sign of the covenant. Therefore we are forced to ask what is the relationship between Abrahamic and the New Covenant. To understand the New Covenant we look at Jeremiah 31:
Jer 31:31 “Behold, the days are coming, declares the LORD, when I will make a new covenant with the house of Israel and the house of Judah,
Jer 31:32 not like the covenant that I made with their fathers on the day when I took them by the hand to bring them out of the land of Egypt, my covenant that they broke, though I was their husband, declares the LORD.
Jer 31:33 For this is the covenant that I will make with the house of Israel after those days, declares the LORD: I will put my law within them, and I will write it on their hearts. And I will be their God, and they shall be my people.
Jer 31:34 And no longer shall each one teach his neighbor and each his brother, saying, ‘Know the LORD,’ for they shall all know me, from the least of them to the greatest, declares the LORD. For I will forgive their iniquity, and I will remember their sin no more.”
The New Covenant would not be like the other covenant. This other covenant is clearly the covenant of Moses “not like the covenant that I made with their fathers on the day when I took them by the hand to bring them out of the land of Egypt,” The covenant made with Israel was the Mosaic not the Abrahamic. Clearly the Mosaic didn’t “replace” the Abrahamic because Galatians tells us we are children of Abraham. The next clause of verse 32 “my covenant that they broke”. The Abrahamic covenant cannot be broken by us because God is the one who passed through the pieces in Genesis 15. The New Covenant is new because Christ has fulfilled the Law and Prophets being under the Covenant of Works.
Children were clearly considered in the covenant with Abraham. And the Mosaic did not get rid of the Abrahamic. We cannot break the Abrahamic. Therefore children are still in the Abrahamic covenant.
What happens to Circumcision?
The next question would be about circumcision. Clearly circumcision we are told is no longer of use.
1 Cor 7:18 Was anyone at the time of his call already circumcised? Let him not seek to remove the marks of circumcision. Was anyone at the time of his call uncircumcised? Let him not seek circumcision. (and Acts 15; Rom 3&4)
If the sign of the Abrahamic Covenant (circumcision) was abrogated then what is the rite of passage into the New Covenant Administration of the Abrahamic? Colossians 2:11
Col 2:11 In him also you were circumcised with a circumcision made without hands, by putting off the body of the flesh, by the circumcision of Christ,
Col 2:12 having been buried with him in baptism, in which you were also raised with him through faith in the powerful working of God, who raised him from the dead.
Circumcision was fulfilled in Christ. Now we associate our inclusion of the Abrahamic with the death and resurrection of Jesus (Baptism). Our children who are still part of the Abrahamic covenant are still in the covenant. Baptism existed prior to circumcision as 1 Peter 3 notes:
1 Pet 3:20 because they formerly did not obey, when God’s patience waited in the days of Noah, while the ark was being prepared, in which a few, that is, eight persons, were brought safely through water.
1 Pet 3:21 Baptism, which corresponds to this, 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,
Baptism is a sign of the death and resurrection of Jesus administered to the family of at least 1 believing parent. Speaking of the Old Testament temple system the author of Hebrews writes:
Heb 9:9 (which is symbolic for the present age). According to this arrangement, gifts and sacrifices are offered that cannot perfect the conscience of the worshiper,
Heb 9:10 but deal only with food and drink and various washings, regulations for the body imposed until the time of reformation.
“various washings” are properly understood as “various baptisms”. Having these baptisms and washings as part of their ceremonious worship already it was no surprise for the Jews to hear Peter say “repent and be baptized, everyone of you, in the name of Jesus, for the remission of sins…for the promise is to you and your children.” The Jews were familiar with this and didn’t respond “What’s baptism?” They understood them as priestly washings and they also understood that this New Covenant would still hold out the promise for them and their children.