The issue is whether salvation is conditional upon water baptism.
It is not.
Yes, Christians do many things AFTER salvation, and water baptism is normally the first. But they are already saved before they are baptized in water, because they are saved by faith, the same as Abraham was.
Water baptism saves us in a figure, which means symbolically. It IS A SYMBOL of salvation because it symbolizes dying to the old sinful life, being buried with Christ, and rising from the dead with Christ.
But symbols aren't real. That's why they're called "symbols", and that's why Peter says "in a figure". It is acted out and we do not actually die, get buried, and rise again when we are baptized in water, but that is what we portray as we act it out.
"Believe on the Lord Jesus Christ and thou shalt be saved." Ok, I have believed on Him and I am saved. What next? Well what did they do next in Acts 2? What did they do next in Acts 10? What did they do next in Acts 16? There's your answer. You're a Christian now, so walk in obedience. Go and be a witness to the world by being baptized in the name of the Lord in water, and show them that you HAVE DIED to the old life by faith, and you HAVE BEEN buried with Christ in the grave by faith, and you HAVE BEEN resurrected with Christ by faith to newness of life, because that IS what HAPPENED in the Spirit when you believed and were saved. Now SHOW IT in a figure. That is obedience and obedience out of love is the hallmark of the Christian life, but obedience doesn't save you - faith does.