Baptism was actually a very important practice in the early church. It is mentioned frequently in the book of Acts.
It is written that Jesus said he would build his church on Peter; and though it doesn't say so explicitly, Peter may have been given the authority to loosen people from their sins through water baptism.
And I also say to you that you are Peter, and on this rock I will build my church, and the gates of Hades will not overpower it! I will give you the keys of the kingdom of heaven, and whatever you bind on earth will be bound in heaven, and whatever you release on earth will be released in heaven.” Matthew 16:18-19
On the day of Pentecost, he exercised this authority to authorize the forgiveness of Israel's sins through water baptism in Christ's name.
And Peter said to them, “Repent and be baptized, each 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. Acts 2:38
So those who accepted his message were baptized, and on that day about three thousand souls were added. Acts 2:41
From that point on, many people in the church baptized others in Christ's name for the forgiveness of sins. Peter opened the door, but it was not his authority to exercise exclusively.
Then as head of the church on earth, he was sent to the gentiles to open the door of salvation to them. Again, he authorized that they be baptized in the name of Jesus for forgiveness of sins.
Surely no one can withhold the water for these [people] to be baptized, who have received the Holy Spirit as we also did!” So he ordered [that] they be baptized in the name of Jesus Christ. Then they asked him to stay for several days. Acts 10:47-48