For, as Doddridge well observes, "What would have been done with the infants, or male children, of Christians ?"--that is, of converted Jews, as well as others.

They could not circumcise them; but their teachers, being spiritually-minded men, knew that circumcision was a seal of faith, not merely of nationality, and must not the converts have required some sign and symbol still for their children?
Now they had long been used to the baptism of proselytes and their children; so that baptizing their own children, as a substitute for circumcising them, could not have been a violent change with those whom Peter's vision of the sheet had taught that the Gentiles should be fellow-heirs.

And when he, in one of his first sermons, said to the whole house of Israel, "Ye are the children of the covenant," and "The promise is unto you and to your children," we can account for their utter silence as to any revocation by Christianity of the right and privilege of applying the initiatory ordinance of religion, for the time being, to a believer's child.
"But," said Mr.Benson, "the Saviour said, 'He that believeth, and is baptized, shall be saved.' The apostles said, 'Repent and be baptized, every one of you.' Show us, now, why this does not prove that repentance and faith were not thus made essential to baptism.

According to these passages, none could be baptized who had not repented and believed.
This would exclude infants.

'Believe, and be baptized;' how do you dispose of that, sir ?" "Very easily," said I.
Mrs.Benson exclaimed, "O, sir, if you can, all my difficulty is at an end!" "Well, then," said I, "in the first place, there is no such requirement in the Bible.