Here is the exact, verbatim message that Peter gave the sinners at Pentecost....The message Peter gave to the Gentiles that believing in Him is for the remission of sins has to be the same message to the Jews, but you are not seeing it in that call to "Repent" which is to turn from unbelief by believing in Him Whom the Jews had crucified in unbelief.
Not sure why you are not seeing it but something is blocking you from reading Peter's words plainly to the Gentiles about how they were to get that remission of sins by believing in Him and what do you know? They got the gift of the Holy Ghost after that, way before water baptism.
38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
Now, what else are we not seeing?