The Bible nowhere says baptism is to be restricted to adults. Some here just conclude that is what it should be taken as meaning, even if the text does not explicitly support such a view. Naturally enough, the people whose baptisms we read about in Scripture (and few are individually identified) are adults, because they were converted as adults. This makes sense, because Christianity was just beginning—there were no "cradle Christians," people brought up from childhood in Christian homes.
Even in the books of the New Testament that were written later in the first century, during the time when children were raised in the first Christian homes, we never—not even once—find an example of a child raised in a Christian home who is baptized only upon making a "decision for Christ." Rather, it is always assumed that the children of Christian homes are already Christians, that they have already been "baptized into Christ" (Rom. 6:3). If infant baptism were not the rule, then we should have references to the children of Christian parents joining the Church only after they had come to the age of reason, and there are no such records in the Bible.
But, one might ask, does the Bible ever say that infants or young children can be baptized? The indications are clear. In the New Testament we read that Lydia was converted by Paul’s preaching and that "She was baptized, with her household" (Acts 16:15). The Philippian jailer whom Paul and Silas had converted to the faith was baptized that night along with his household. We are told that "the same hour of the night . . . he was baptized, with all his family" (Acts 16:33). And in his greetings to the Corinthians, Paul recalled that, "I did baptize also the household of Stephanas" (1 Cor. 1:16).
In all these cases, whole households or families were baptized. This means more than just the spouse; the children too were included. If the text of Acts referred simply to the Philippian jailer and his wife, then we would read that "he and his wife were baptized," but we don’t. Therefore his children must have been baptized as well. The same applies to the other cases of household baptism in Scripture.
Granted, we do not know the exact age of the children; they may have been past the age of reason, rather than infants. Then again, they could have been babes in arms. More probably, there were both younger and older children. Certainly there were children younger than the age of reason in some of the households that were baptized, especially if one considers that society at this time had no reliable form of birth control. Furthermore, given the New Testament pattern of household baptism, if there were to be exceptions to this rule (such as infants), they would be explicit.