But about 36 C.E. God directed Peter to go to the home of the Gentile Cornelius, a Roman army officer, and by pouring out His holy spirit on Cornelius and his household, showed Peter that Gentiles could now be accepted for water baptism. (Ac 10:34, 35, 44-48)

An argument is made by some in favor of infant baptism. They refer to the instances where ‘households’ were baptized, such as the households of Cornelius, Lydia, the Philippian jailer, Crispus, and Stephanas. (Ac 10:48; 11:14; 16:15, 32-34; 18:8; 1Co 1:16) They believe that this implies that small babies in those families were also baptized. But, in the case of Cornelius, those who were baptized were those who had heard the word and received the holy spirit, and they spoke in tongues and glorified God; these things could not apply to infants. (Ac 10:44-46) Lydia was “a worshiper of God, . . . and Jehovah opened her heart wide to pay attention to the things being spoken by Paul.” (Ac 16:14) The Philippian jailer had to “believe on the Lord Jesus,” and this implies that the others in his family also had to believe in order to be baptized. (Ac 16:31-34) “Crispus the presiding officer of the synagogue became a believer in the Lord, and so did all his household.” (Ac 18:8) All of this demonstrates that associated with baptism were such things as hearing, believing, and glorifying God, things infants cannot do.