There are multiple examples of entire households being baptized in Acts 16. Christians could just assume that one of these households had an infant child in it, but even if they do not, they can still conclude that infant baptism is legitimate.
1 Peter 3:20-21
“who formerly were disobedient, when once the Divine longsuffering waited in the days of Noah, while the ark was being prepared, in which a few, that is, eight souls, were saved through water. There is also an antitype which now saves us—baptism (not the removal of the filth of the flesh, but the answer of a good conscience toward God), through the resurrection of Jesus Christ,”
Peter tells us that Noah and his family were saved through the waters of the flood (which symbolizes baptism). However, Genesis 6 tells us that only Noah was righteous, not his family. And because of Noah’s righteousness, his entire family received the benefit. They were set apart, sanctified, and were made holy. This is also supported by Paul.
1 Corinthians 7:14
“For the unbelieving husband is sanctified by the wife, and the unbelieving wife is sanctified by the husband; otherwise your children would be unclean, but now they are holy.”
It is possible to be part of God’s kingdom without having personal salvation. Many Christians will object because they believe that baptism is an outward profession of faith. However, circumcision was also a sign of personal faith (Romans 4:11-12). And Paul explains that baptism is the new circumcision. That Christians were circumcised by Christ through baptism. Therefore, since circumcision was not an exclusive profession of faith, it is the same with baptism.
Colossians 2:11-12
“In Him you were also circumcised with the circumcision made without hands, by putting off the body of the sins of the flesh, by the circumcision of Christ, buried with Him in baptism, in which you also were raised with Him through faith in the working of God, who raised Him from the dead.”
Acts 2:38-39
“‘Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit. For the promise is to you and to your children’”
CIRCUMCISION:
-Sign of Covenant
-With hands
-For both believers and their children
BAPTISM:
-Sign of Covenant
-With water
-For both believers and their children
Some people might object to this by saying that God commanded Abraham to circumcise his descendants, but He did not command Christians to circumcise their children. The answer to this is simple: there is no need to repeat the command! The Old Covenant is replaced by the New Covenant,
and baptism replaces circumcision. This expresses Kingdom Theology. Think of it like this: When a person immigrates to another country, they go through the process of becoming a citizen. However, a person born to a citizen automatically becomes a citizen. This is not to say that all people who were baptized as infants are Christians; but rather, they are part of God’s kingdom in a sense. Not everyone who was circumcised was saved either, but they were still part of the kingdom of God in a sense. You can be a soldier, fighting for personal motives, and still help God’s kingdom (Philippians 1:15-18).
John Calvin himself said that Satan will do his best to ruin paedobaptism. He says, “For it is of importance to observe what Satan means by all this craft, viz., to rob us of the singular blessing of confidence and spiritual joy, which is hence to be derived, and in so far to detract from the glory of the divine goodness.”