Look at what happened when Peter preached the gospel to Cornelius.
While Peter was still saying these things, the Holy Spirit fell on all who heard the word. And the believers from among the circumcised who had come with Peter were amazed, because the gift of the Holy Spirit was poured out even on the Gentiles. For they were hearing them speaking in tongues and extolling God. Then Peter declared, “Can anyone withhold water for baptizing these people, who have received the Holy Spirit just as we have?” And he commanded them to be baptized in the name of Jesus Christ. Then they asked him to remain for some days.
Acts 10:44-48 ESV
While Peter was still preaching his listeners were saved and received the Holy Spirit. It was only after these things happened that they were baptized in water. Also, look at the reason John wrote his gospel.
Now there are also many other things that Jesus did. Were every one of them to be written, I suppose that the world itself could not contain the books that would be written.
John 21:25 ESV
If John was written to show how to receive eternal life and water baptism was necessary, then water baptism must be commanded in the book. In fact, there is no such command. John records the fact that both John the Baptist and Jesus baptized their converts but there is no command to be baptized. When Jesus was addressing the unsaved he frequently told them they must believe on him but he never told them they needed to be baptized in water.
Ephesians 2:8-10 says, For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, not a result of works, so that no one may boast. For we are his workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them.
We neither receive or keep our salvation by anything we do. It is a gift of God and Romans 11:29 says, For the gifts and the calling of God are irrevocable. You probably know of people who have professed to be Christians but later denied the faith and went on to live lives that proved they weren't saved. These people didn't lose their salvation but were never saved in the first place. Perhaps they were victims of the easy believism gospel.