Peter explained what happens at baptism when he said, “Repent, and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins; and you shall receive the gift of the Holy Spirit” (Acts 2:38). But he did not restrict this teaching to adults. He added, "For the promise is to you and to your children…
The Council of Carthage, in 253, condemned the opinion that baptism should be withheld from infants until the eighth day after birth. Later, Augustine taught, “The custom of Mother Church in baptizing infants is certainly not to be scorned . . . nor is it to be believed that its tradition is anything except apostolic” (Literal Interpretation of Genesis 10:23:39 [A.D. 408]).
catholic.com/library/Infant_Baptism.asp
How would a woman be circumcised?
Easy for them to be baptised
scripturecatholic.com/baptism.html#baptism-III
Baptism replaces circumcision
Gen. 17:12, Lev. 12:3 - these texts show the circumcision of eight-day old babies as the way of entering into the Old Covenant - Col 2:11-12 - however, baptism is the new “circumcision” for all people of the New Covenant. Therefore, baptism is for babies as well as adults. God did not make His new Covenant narrower than the old Covenant. To the contrary, He made it wider, for both Jews and Gentiles, infants and adults. If Paul meant to exclude infants, he would not have chosen circumcision as a parallel for baptism.
Let the children come to me
Matt. 18:2-5 - Jesus says unless we become like children, we cannot enter into heaven. So why would children be excluded from baptism?
Matt 19:14 - Jesus clearly says the kingdom of heaven also belongs to children. There is no age limit on entering the kingdom, and no age limit for being eligible for baptism.
Mark 10:14 - Jesus says to let the children come to Him for the kingdom of God also belongs to them. Jesus says nothing about being too young to come into the kingdom of God.
Luke 18:15 – Jesus says, “Let the children come to me.” The people brought infants to Jesus that he might touch them. This demonstrates that the receipt of grace is not dependent upon the age of reason.
Baptism without faith
Mark 16:16 - Jesus says to the crowd, “He who believes and is baptized will be saved.” But in reference to the same people, Jesus immediately follows with “He who does not believe will be condemned.” This demonstrates that one can be baptized and still not be a believer. This disproves the Protestant argument that one must be a believer to be baptized. There is nothing in the Bible about a “believer’s baptism.”
Households included infants
Acts 2:38 - Peter says to the multitude, “Repent and be baptized…” Protestants use this verse to prove one must be a believer (not an infant) to be baptized. But the Greek translation literally says, "If you repent, then each one who is a part of you and yours must each be baptized” (“Metanoesate kai bapistheto hekastos hymon.”) This, contrary to what Protestants argue, actually proves that babies are baptized based on their parents’ faith. This is confirmed in the next verse.
Acts 2:39 - Peter then says baptism is specifically given to children as well as adults. “Those far off” refers to those who were at their “homes” (primarily infants and children). God’s covenant family includes children. The word “children” that Peter used comes from the Greek word “teknon” which also includes infants.
Luke 1:59 - this proves that “teknon” includes infants. Here, John as a “teknon” (infant) was circumcised. See also Acts 21:21 which uses “teknon” for eight-day old babies. So baptism is for infants as well as adults.
There is not one word in Scripture about baptism being limited to adults. Acts 16:15 - Paul baptized Lydia and her entire household. The word “household” comes from the Greek word “oikos” which is a household that includes infants and children.
Acts 16:15 - further, Paul baptizes the household based on Lydia’s faith, not the faith of the members of the household. This demonstrates that parents can present their children for baptism based on the parents’ faith, not the children’s faith.
2 Thess. 3:10 - if anyone does not work let him not eat. But this implies that those who are unable to work should still be able to eat. Babies should not starve because they are unable to work, and should also not be denied baptism because they are unable to make a declaration of faith.
Forgiveness based on another’s faith
Matt. 9:2; Mark 2:3-5 - the faith of those who brought in the paralytic cured the paralytic’s sins. This is an example of the forgiveness of sins based on another’s faith, just like infant baptism. The infant child is forgiven of sin based on the parents’ faith.
Matt. 8:5-13 - the servant is healed based upon the centurion’s faith. This is another example of healing based on another’s faith. If Jesus can heal us based on someone else’s faith, then He can baptize us based on someone else’s faith as well.
Mark 9:22-25 - Jesus exercises the child’s unclean spirit based on the father’s faith. This healing is again based on another’s faith.
1 Cor. 7:14 – Paul says that children are sanctified by God through the belief of only one of their parents.
Exodus 12:24-28 - the Passover was based on the parent’s faith. If they did not kill and eat the lamb, their first-born child died.
Joshua 5:2-7 - God punished Israel because the people had not circumcised their children. This was based on the parent’s faith. The parents play a critical role in their child’s salvation.