Not sure it all can be neatly "formulized" in NT...
For example, Jesus told Saul to be baptized...and calling on His Name was interwoven at same time (if not after)
16 And now what are you waiting for? Get up, be baptized and wash your sins away, calling on his name.’ (Acts 22)
Secondly, there seemed to be some pretty almost instant across-the-board family-wide baptisms (Acts 16:14-15, 33). These were pretty sudden turn-abouts with seemingly little to none indications that these were a slow-cooking family member-by-family member "canvass" of individual faith beliefs...IoW, it's pretty easy for Westernized Evangelicals to insert their individualistic confession of faith into Biblical scenes enacted in corporate minded Middle Eastern cultures.
Also, were not given a complete formula that applied each time to all of the baptisms as recorded in Acts 2:41; 8:37; 9:5-6, 17-18; 10:47; 11:16-17; 16:14-15; 16:33; Acts 18:8; 1 Cor. 1:16; Gal. 3:26-27).
I mean receiving the Holy Spirit -- vital for a real REbirth -- is mentioned in Acts 9, 10, & 11...but not in the other references above.
I have to agree that there is no formula. It seems this may be so when we all get into “discussions” we all rush to the bible and delve into the word of God. What better way for the Lord to get people into bible studies, overcoming those who think they have a corner on Christian belief.
It has often been said the Bible is the most purchased book in America, and the least read. But not here!