John 1:12 tells us what is necessary to become a Christian. “But to all who received Him, who believed in His name, He gave power to become children of God.” The word “believe” in that verse is the same word that John uses 99 times in his gospel. And it means to fully rely on, to fully trust in Jesus.
All of Romans shows that a person comes into a relationship with God by faith, by believing. Paul goes into great lengths in Romans 2-4 (especially 4) to show that Abraham was saved, was declared righteous by God, because of his faith in God — not because of his circumcision. In verse 2, Paul refers to circumcision as “works”. If Abraham had been made righteous by circumcision, then he would have something to boast about (4:2) but not before God. God accepts people and brings them into a relationship with Him based on their faith….”trusting Him who justifies the ungodly.” (4:5)
There is a spiritual baptism which is a part of salvation. When we believe in Him we are baptized into Christ (Romans 6:3,4). This is a very real and spiritual baptism, just like being crucified with Him is also spiritual (not literal) (Rom 6:5).
While all believers in Jesus should follow His command to be baptized (Matthew 28:19), it is not essential for, nor equivalent to salvation. Salvation is by grace through faith alone (Ephesians 2:8-9, 1John 5:11-13, John 3:16, Luke 7:50, Romans 10:9-10, Acts 16:30-31, Romans 1:16-17, 2Timothy 3:15, 1Peter 1:3-5,9). Water baptism is an outward sign of an inner transformation and cleansing that identifies one with the body of Christ (Romans 6:1-16).
When one is baptized by water, it is to be an identifying with the body of Christ, a testimony to others that this person believes in Jesus and belongs to Him. It is not the baptism that saves them, but their faith in Jesus. It’s similar to walking to the front of a church at a gospel presentation. The walk down the aisle is not what saves a person, but their faith in Jesus. Water baptism or public confession is acknowledging what has already become true of this person – that they believe in Jesus. John 15 and other places talk about Jesus being in us as soon as we believe. Much of Scripture talks about Him coming into our lives (Rom 8:9-10) when we believe.
From the moment we receive Christ we are baptized by the Spirit. First Corinthians 12:12-13 says “For even as the body is one and yet has many members, and all the members of the body, though they are many, are one body, so also is Christ. For by one Spirit we were all baptized into one body, whether Jews or Greeks, whether slaves or free, and we were all made to drink of one Spirit.” And Ephesians 1:13-14 says, “In Him you also, who have heard the word of truth, the gospel of your salvation, and have believed in him, were sealed with the promised Holy Spirit, which is the guarantee of our inheritance until we acquire possession of it, to the praise of His glory.” Romans 8 also talks extensively about the Spirit dwelling in those who believe.