In the early Church, new conversions were happening by the scores. The apostles would not have had time to baptize all these people themselves, so they appointed deacons to baptize for them. That is why Paul says he was not sent to baptize (1 Cor 1:17). But this does not mean that water baptism had no part in Paul's gospel. On the contrary, Paul was water baptized himself (Acts 9:18, Acts 22:16), and Paul clearly taught water baptism:
Acts 16:14-15
And a certain woman named Lydia, a seller of purple, of the city of Thyatira, which worshipped God, heard us: whose heart the Lord opened, that she attended unto the things which were spoken of Paul. And when she was baptized, and her household, she besought us, saying, If ye have judged me to be faithful to the Lord, come into my house, and abide there. And she constrained us.
Acts 16:28-33
28 Paul called with a loud voice, saying, “Do yourself no harm, for we are all here.” 29 Then he called for a light, ran in, and fell down trembling before Paul and Silas. 30 And he brought them out and said, “Sirs, what must I do to be saved?” 31 So they said, “Believe on the Lord Jesus Christ, and you will be saved, you and your household.” 32 Then they spoke the word of the Lord to him and to all who were in his house. 33 And he took them the same hour of the night and washed their stripes. And immediately he and all his family were baptized.
Acts 18:5, 8
Paul was pressed in the spirit, and testified to the Jews that Jesus was Christ...And Crispus, the chief ruler of the synagogue, believed on the Lord with all his house; and many of the Corinthians hearing believed, and were baptized.
Acts 19:4-5
Paul said, “John indeed baptized with a baptism of repentance, saying to the people that they should believe on Him who would come after him, that is, on Christ Jesus.” When they heard this, they were baptized in the name of the Lord Jesus.
Paul did not always perform water baptisms personally, but he clearly taught the practice of water baptism.