Yet you are he who took me from the womb; you made me trust you at my mother's breasts. On you was I cast from my birth, and from my mother's womb you have been my God. (Psalm 22)
It seems clear to me that everyone in Israel was Presbyterian when it came to the status of the kids. In virtue of being born (conceived? cf 'womb' above) into a family that was in covenant with God (an Israelite family), a child was considered a member of the covenant. There were no conversion experiences expected for such children once they reached some supposed 'age of accountability'. (Find one of such a child in the OT - or the NT for that matter.) From birth (at least) the covenant God of Israel was their God. Much more needs to be said, but at least this much seems obvious.
So, where does it say that this all changed once Jesus arrived?
An unpolished thought