To me from my understanding, baptism is something one does as an adult as a public showing of your obedience to Jesus. It’s a public affirmation of your faith in him.
I have never seen any scripture indicating that babies were baptized.
Whole households were baptized as recorded in scripture. Did they somehow keep the babies and infants outside the house while the sacrament was administered?
Matthew 19:14-15 "Then they brought children to him, so that he might lay his hands on them in prayer; and his disciples rebuked them for it. 14 But Jesus said, Let the children be, do not keep them back from me; the kingdom of heaven belongs to such as these. 15 And so he laid his hands on them, and went on his way. "
But an RC can see what they want, and thus 3 simple mentions of household baptisms (Acts 16:33; 18:8; 1Cor. 1:16) is proffered as evidence for paedobaptism, yet the stated requirement is that of repentant wholehearted faith, (Acts 2:28; 8:36,37) which an infant cannot fulfill.
And while we suffer from the effects of Adam's sin, eternal damnation is based upon what one is personally culpable for, not that of our fathers. Dt. 24:16; 2Ki 14:5,6; 2Ch 25:4; Jer 31:29,30; Eze 18:20)
In addition, where more information is provided other than a cursory mean such as "I baptized also the household of Stephanas," then it records or indicates that those baptized were those who could hear the word and thus respond. (Acts 2:41; 8:12; 10:43-47; 19:4,5; 16:32; 22:16)
“I have never seen any scripture indicating that babies were baptized.” — I’ve never seen any scripture indicated that only adults were. As a matter of fact, scripture is more supportive of the Catholic faith’s teaching of infant baptism. See Acts 16:15, 16:33; 1 Cor 1:16. for references to whole households being baptized.