“It also makes it plain that baptism must follow conversion.”
I agree, more so than you do I suspect. I would cheerfully see someone baptized the day they convert. But it FOLLOWS conversion, which is the new birth.
“44While Peter was still saying these things, the Holy Spirit fell on all who heard the word. 45And the believers from among the circumcised who had come with Peter were amazed, because the gift of the Holy Spirit was poured out even on the Gentiles. 46For they were hearing them speaking in tongues and extolling God. Then Peter declared, 47 “Can anyone withhold water for baptizing these people, who have received the Holy Spirit just as we have?” 48And he commanded them to be baptized in the name of Jesus Christ.” - Acts 10
This is where we agree, because that part IS in the scripture: conversion of an adult makes baptism of an adult, and of his children, possible.
That conversion is in itself a new birth contradicts John 3:3-5, where "birth of the water" is spoken about in the context of being born again.