The key is found in the verse that is missing in many Bible translations
Acts 8:37 And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God.
Note that the belief that came, before water baptism was done, was based on believing Jesus Christ is the Son of God, which is the foundation of the gospel of the kingdom (John 20:30-31, Mark 16:16).
There was no need for any of them to believe that "Jesus died for my sins and rose again on the 3rd day for my justification" (1 Cor 15:1-4, Romans 4:24-25) which is the foundation of our gospel of grace that is valid for us today.
That is good enough indication to me that, while water baptism was certainly necessary for salvation during the 4 gospels and early Acts, it is no longer necessary under the gospel of grace committed to the apostle Paul for us gentiles (1 Corithians 1:17).
For Christ sent me not to baptize, but to preach the gospel: not with wisdom of words, lest the cross of Christ should be made of none effect.