Peter's message was what they heard.
They believed it. They were convicted but didn't know what to do. Peter told them.
They responded and were baptized.
I'll answer your question with this....when was Cornelius saved? Before or after being baptized?
I don’t think the physical act of immersion is what saves you, either.
Before, you said that Peter told them to believe, and used Ac. 2.37-38 as a proof text. You’re right now that you say they heard Peter’s message and believed. Thus, he didn’t tell them to hear or believe in Ac. 2.37-38, as you asserted.
Then Peter told them to be baptized for the remission of sins. You say they responded and were baptized.
Question: Were they baptized for the reason Peter said, for the remission of their sins? Or did they say, “physical immersion doesn’t save you, and what about Cornelius?”
Were they Christians before they had the remission of their sins, like the fellow in your original post?
Since baptism puts one into Christ (Gal. 3.27, Rom. 6.3-4), was he in Christ before he was baptized, and therefore saved outside of Christ?
Since baptism puts one into the body of Christ, I Cor. 12.13, was he in the body of Christ before he was baptized, and therefore saved outside the body of Christ?
Cornelius heard Peter tell him (Ac. 10.48) “and he commanded them to be baptized in the name of Jesus Christ.”
What was baptism in the name of Christ, ealgeone? Wasn’t that the baptism in Ac. 2.37-28 that you quoted? “What must we do? Repent and be baptized every one of you in the name of Jesus Christ for the remission of sins.”
I don’t think Cornelius had the remission of his sins before his baptism, do you? The Holy Spirit falling on that group didn’t give them remission of sins, either, did it?