Paul wrote almost half of the New Testament, he is the only author in Scripture that explains exactly how to be saved in detail.
Show me one time where Paul mentions water baptism is necessary for salvation.
Don't risk your eternal life on what Luke said in passing as to what Peter said. That is not and was not meant to be an explanation of salvation.
It was what was said with no explanation whatsoever.
What Peter actually said was, "repent and be baptized BECAUSE OF the forgiveness of sins."
The forgiveness of sins is in the repenting, not the water baptism
So, no one got saved by Jesus' preaching? No one was saved before Paul? I gave you Paul's words, 'He saved us by the bath of regeneration and renewing of the Holy Spirit. The only bath in the Christian faith is water baptism.
Don't buy the "because of" argument. Robertson tried to make that argument and Mantley took him to task. Since then quite a few other Scholars have refuted Robertson's argument including one of the prominent Scholars of today, Daniel Wallace. Robertson tried the same thing many others do to diminish baptism.
But, let's look at Paul's words.
25 Husbands, love your wives, even as Christ also loved the church, and gave himself for it; 26
That he might sanctify and cleanse it with the washing of water by the word, 27 That he might present it to himself a glorious church, not having spot, or wrinkle, or any such thing; but that it should be holy and without blemish.
The Holy Bible: King James Version, Electronic Edition of the 1900 Authorized Version. (Bellingham, WA: Logos Research Systems, Inc., 2009), Eph 5:25–27.
It literally reads, that He might sanctify and cleanse it with the bath of water in the word. There's a bath or water. In what word? The word, translated word is rhema. It's the spoken word. So, what spoken word speaks of a bath or water?
19 Go ye therefore, and teach all nations,
baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: 20 Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you alway, even unto the end of the world. Amen.
The Holy Bible: King James Version, Electronic Edition of the 1900 Authorized Version. (Bellingham, WA: Logos Research Systems, Inc., 2009), Mt 28:19–20.
Luke was Paul's traveling companion, so much of what he learned he learned from Paul. Here is Luke's account of Paul's encounter with Ananias.
15 For thou shalt be his witness unto all men of what thou hast seen and heard. 16 And now why tarriest thou? arise, and
be baptized, and wash away thy sins, calling on the name of the Lord.
The Holy Bible: King James Version, Electronic Edition of the 1900 Authorized Version. (Bellingham, WA: Logos Research Systems, Inc., 2009), Ac 22:15–16.
Here, "be baptized" is a command and it's in the middle voice. In the middle voice, the subject both does and receives the action of the verb. In other words, he's doing it to himself. In this passage, Ananias is commanding Paul to be baptized. In this, he is both doing and receiving the action. Note that in this baptism he is
washing. That entails water. He is washing away his sins. So, water baptism washes away sins. Isn't that what Peter said? Repent and be baptized for the forgiveness of sins? Also in this water, there is a calling on the name of the Lord. Didn't Peter also say this?
18 For Christ also suffered once for sins,
the just for the unjust,
in order that he could bring you to God,
being put to death in the flesh,
but made alive in the spirit,
19 in which also he went and proclaimed to the spirits in prison,
20 who were formerly disobedient, when the patience of God waited in the days of Noah, while* an ark was being constructed, in which a few—that is,
eight souls—were rescued through water. 21 And also, corresponding to this, baptism now saves you, not the removal of dirt from the flesh,
but an appeal to God for a good conscience through the resurrection of Jesus Christ, 22 who is at the right hand of God, having gone into heaven, with angels and authorities and powers having been subjected to him.
W. Hall Harris III et al., eds., The Lexham English Bible (Bellingham, WA: Lexham Press, 2012), 1 Pe 3:18–22.
In both passages, we see that in water baptism there is an appeal made to God. Notice in Ananias' statement it's all about the physical part of baptism. He didn't explain the part that God plays in it. The point is that water baptism is the point where one enters the faith. It's where sins are forgiven and an appeal is made to God