your own question gives the answer:
Acts 16:29 Then he called for a light, and sprang in, and came trembling, and fell down before Paul and Silas,
Acts 16:30 And brought them out, and said, Sirs, what must I do to be saved?
Acts 16:31 And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.
Acts 16:32 And they spake unto him the word of the Lord, and to all that were in his house.
Acts 16:33 And he took them the same hour of the night, and washed [their] stripes; and was baptized, he and all his, straightway.
it isn’t age, it is BELIEF
Can a month old infant believe anything?
Should you trust a 4 year old when they say they believe something that they have no idea happened?
If a small child can express a belief and back it up with what they were taught...then they believe
but a baby...that is clearly not Biblical, nor is some sort of grace applied to anyone who is baptised, nor is salvation through baptism in any manner
So the words... ‘and thy house’ are irrelevant?
The confirmation process... Which occurs once a child is of an age a reason address the issue of belief but it is clear that infant baptism is in fact biblical.
One more question... Any thoughts on John chapter 6 from about verse 50 until the end?