The problem here is a western mindset trying to understand and take apart something that was never meant to be separated. Baptisms were always done as part of a conversion in the bible. For example, when Philip preaches to the Ethiopian eunuch what is his response to the gospel? “Here is some water. What would stop me from being baptized?” So, we know what gospel was being preached by Philip. The same gospel being preached by Peter in Acts 2:38. Repent and be baptized for the forgiveness of your sins… but we use Cornelius house story as an example to try to split these events and ask ourselves the exact point salvation begins. There are scriptures that can be used to argue either way. Why? Because we are attempting to split salvation and baptism. something not done in the early church. Baptisms were done immediately after believing and repenting.
Many people use Paul’s letters like Romans 10:9-10 to support their case even though the book of Romans is written to disciples who were baptized already. They also fail to see the word immediately here: Acts 16:33 At that hour of the night the jailer took them and washed their wounds; then immediately he and all his household were baptized. We see Paul also baptized immediately! At Cornelius house the response to seeing they were filled with the Holy Spirit… and Peter gave orders that they be baptized. Instead of dissecting the exact moment of salvation, let us start following the bible and do baptisms immediately. We can know the answer for sure once we are in heaven with Jesus but for now let us follow what Philip, Peter and Paul did.
I do agree on is that just dunking someone in water will not save you. We call this a ceremonial baptism. Instead of focusing on the exact moment salvation begins we should rather be focusing on what Jesus does in a baptism that is not just a ceremony. In Colossians 2 we see baptism is a circumcision done by Jesus himself!! In Romans 6:3-6 we see we are united with Christ in his death in baptism! In 1 Corinthians 10 we see baptism as a deliverance from slavery for Israel.
Just dunking someone in water will not save them. Instead we must teach Romans 6:3-6 that when they go down in the water they are united with Christ in his death. That their old sinful spirit is buried with Christ. The old spirit man dies in the water. We are a spirit and live in a body and we a soul. The soul (emotions, personality) and spirit are different however many use these as meaning the same thing. God makes a distinction in the bible. That beings aid the bible does sometimes use these terms interchangeably based upon the bible translation and the context in the scripture.
One final point. Many people have heard it said that baptism is an outward sign of an inward change. That isn’t in your bible! When you hear this it means the person baptizing you sadly doesn’t really believe Colossians 2:11-14 and Romans 6:3-6. How can we be united with Christ in his death in baptism if we were already born again through a sinner’s prayer 2 or 3 years earlier? How was the old man put to death? Where is the sinner’s prayer in your bible? Come on my brothers and sisters. Let us drop these errors passed on to us by the previous generation of evangelists. I respect their work and even quote them here from time to time but let us go back to the bible and follow it as best we can.