"Now when they ["Jews, devout men, from every nation under heaven", v. 5] heard this, they were cut to the heart, and said to Peter and the rest of the apostles, "Men and brethren, what shall we do?" Then Peter said to them, "Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit." (Acts 2)
In response to the question "Sirs, what must I do to be saved?" Paul told the (gentile) Philippian jailer, "Believe on the Lord Jesus Christ, and you will be saved, you and your household." {No mention of baptism in Paul's response.}
A dispensationalist might say that repentance and baptism are kingdom requirements, while grace/faith are church age requirements.
Of course that answer would be wrong, but you could try it.
The fact is that men in the Bible were saved prior to being baptized with water.
"While Peter was still speaking these words, the Holy Spirit fell upon all those who heard the word. And those of the circumcision who believed were astonished, as many as came with Peter, because the gift of the Holy Spirit had been poured out on the Gentiles also. For they heard them speak with tongues and magnify God. Then Peter answered, "Can anyone forbid water, that these should not be baptized who have received the Holy Spirit just as we have?" And he commanded them to be baptized in the name of the Lord. Then they asked him to stay a few days." (Acts 10:44ff)
Was it the water that saved them, or the indwelling Holy Spirit? Baptism was the outward sign and seal of God's saving grace that brought faith and salvation to the believer.
Actually, the Holy Spirit fell on Cornelius and his family to show the Jews that Gentiles would also be accepted by God. There are not multiple ways to salvation in the New Testament church. There is only one. And in all 10 stories in Acts in which people are saved, baptism is mentioned in every one of them. Why do you think that is?
The issue in Acts 2:38 is not the water baptism, it is the message that is being preached.
In Acts 2:38 you do not have Christ dying for anyone's sins.
As is the Gospel message today (1Cor.15:3-5)
Peter is talking about David and the promise of his seed ruling over Israel.
That a different Gospel was being preached (John the Baptist) is shown in Acts 18 where Apollos has to be shown 'the way of God more perfectly' and in Acts 19, where Paul encounters 12 disciples who had believed John's Gospel but had not received the Holy Ghost (Acts 19:3-7)
Acts 16:30-33 Sirs, what must I do to be saved?
v.32 then they spoke the word of the Lord to him and to all the others in his house.
v. 33 ...then immediately he and all his family were baptized.
Stop quoting scripture out of context!