Jesus said:
Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age. Matthew 28:19-20.
Jesus instituted baptism, and even told His disciples that's how they were to go out to all nations and make new disciples (baptizing and teaching). Since it was instituted by Jesus, we know that our Lord is the one at work in baptism.
Here is another verse saying the same thing:
Mark 16:15-16. And He said to them, "Go into all the world and preach the gospel to every creature. He who believes and is baptized will be saved; but he who does not believe will be condemned.
In Biblical accounts of Baptism, there was not a lengthy delay between conversion and Baptism (e.g. Acts 2, Acts 8:26-40, Acts 9:-17, Acts 22:1-16, Acts 16:33). They went hand in hand.
What does baptism do for us:
Galatians 3:27. For all of you who were baptized into Christ have clothed yourselves with Christ.
Acts 22:16. And now what are you waiting for? Get up, be baptized and wash your sins away, calling on his name.
Acts 2:37-39. Now when they heard this they were cut to the heart, and said to Peter and the rest of the apostles, "Brothers, what shall we do?" And Peter said to them, "Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit. For the promise is for you and for your children and for all who are far off, everyone whom the Lord our God calls to himself."
Titus 3:5. He saved us, not because of works done by us in righteousness, but according to his own mercy, by the washing of regeneration and renewal of the Holy Spirit.
Corinthians 12:13. 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.
1 Corinthians 6:11. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and by the Spirit of our God.
Mark 16:16. Whoever believes and is baptized will be saved, but whoever does not believe will be condemned.
Eph. 5:26. Christ loved the church and gave Himself up for her to make her holy, cleansing her by the washing with water through the word.
Colossians 2:11-12. In Him you were also circumcised with a circumcision made without hands, in the removal of the body of the flesh by the circumcision of Christ, having been buried with Him in Baptism, in which you were also raised up with Him through faith in the working of God, who raised Him from the dead.
Romans 6:3-10. Or do you not know that all of us who have been baptized into Christ Jesus have been baptized into His death? Therefore we have been buried with Him through Baptism into death, so that as Christ was raised from the dead through the glory of the Father, so we too might walk in newness of life. For if we have become united with Him in the likeness of His death, certainly we shall also be in the likeness of His resurrection, knowing this, that our old self was crucified with Him, in order that our body of sin might be done away with, so that we would no longer be slaves to sin; for he who has died is freed from sin. Now if we have died with Christ, we believe that we shall also live with Him, knowing that Christ, having been raised from the dead, is never to die again; death no longer is master over Him. For the death that He died, He died to sin once for all; but the life that He lives, He lives to God.
There is one baptism, not two separate ones:
One Lord, one faith, one baptism Ephesians 4:5
Don't focus on the water, but the promises that are attached, as per the verses above. God is at work in baptism, not yourself. "Be baptized" is passive meaning you aren't doing something, but something is being done to you. That's God at work.
Baptism is connected to the cross where your sins were won! God uses those waters of baptism to give you the promises He wants to bring to you: washing away your sin, clothing you in Jesus and giving you the gift of the Holy Spirit. It's not a new forgiveness, it's the forgiveness won at the cross and given to you. It's Jesus reaching through the waters to clothe you in His righteousness. It's the Holy Spirit dwelling within you to keep you in the truth faith and sanctifying you.
God is so wonderful to us to bring us those blessings in baptism! One baptism, not two.