The context in 1 Cor. 1 is that everyone is baptized in the name of Jesus. The irony is that if they were baptized by St. Paul, then, he rhetorically concludes, they’d think that he, Paul, is the head of the Church.
That Paul sees his role not as a baptizer but as preacher is in keeping with his intellect and temperament; he is not against people getting baptized at all.
Acts 2:36-38 36 "Therefore let all the house of Israel know assuredly that God has made this Jesus, whom you crucified, both Lord and Christ." 37 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?" 38 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.
Peter preached the Holy Spirit brought conviction then Peter said repent be baptized and receive the Holy Spirit.
Without conviction and repentance their can not be the baptism of water and Spirit.
How many do you know followed that prescribed order?