Now when they 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. For the promise is to you and to your children, and to all who are afar off, as many as the Lord our God will call." And with many other words he testified and exhorted them, saying, "Be saved from this perverse generation."
Acts 2:37-40
When the believers in the crowd asked Peter “what shall we do?” his reply was “repent…and be baptized.” He didn’t mention believe. Why not, and is baptism necessary for salvation?
First, narratives are not the basis of doctrine. While they accurately record what was said and done, they do not explain everything, nor are they a source of doctrine unless passages that are clearly doctrinal, affirm as doctrine what a narrative passage appears to say. Remember that.
Second, the clear teaching of the New Testament is that faith is not only essential for salvation, it is the singular main event (John 6:28-29, Ephesians 2:4-9, Romans 3:28, 5:1—and many more!)
Third, baptism is a command, making it necessary to obey. But baptism is not necessary in order to be saved (any more than any other command in Scripture that must be obeyed), Rather it is a command that must be obeyed by those who are saved—by grace alone, through faith alone, in Christ alone, for the glory of God alone.
That brings up a fourth point. What about the many who are born again by the grace of God who have not been, and who have no particular plan to be, baptized? These may indeed be saved. But unless there is a biblically defensible reason why they have not been, or are not planning to be baptized, they must be or they remain in disobedience to a most fundamental command given to all believers. (There is one argument that not all accept, which may be legitimate for “delaying,” not for “refusing” baptism. Some may contend that due to a youthful lack of understanding, a person could be counseled to wait until he/she learns a bit more and can therefore give a clearer profession of faith.)
No one is saved by being baptized, but saved people must be baptized.