Then those who gladly received his word were baptized;
JLB
First of all, Peter at the time of this preaching, didnt have the revelation of the Grace of God, as this was given to Paul many years later by Jesus himself.
So, Peter was preaching the typical jewish water baptism theology (John the Baptist), as that is all Peter KNEW at that time, and this explains why Acts 2:38 is not the Gospel of the Grace of God, that Paul taught the Church later on.
Also notice that after they received the word they were baptized.
This means, they heard the word, believed (Faith cometh by hearing).. and were SAVED, and then they hit the water.
This is always the same in the NT.........a person hears the word, believes the word, and God saves them, and then they are W-baptized as this is the symbolic "old man dying, new man rising".
Look at your NT......notice that water always FOLLOWS salvation.
"for as many as heard the word and believed it, gave HE them power to become the Sons of God".
No water, just Word mixed with Faith....as water is just a symbol of the conversion that has already occurred by New Birth.
You get Saved and THEN you get water baptized.