I believe you CAN prove the existence of God. But…
Believing that Jesus is the son of God, that there is a holy Trinity, or that God offers salvation are all articles of faith which cannot be scientifically proven.
I do believe that Jesus is/was/always will be the Son of God, there is a Holy Trinity:Father, The Word, The Holy Ghost and these three are one, and salvation is freely offered through the perfect sacrifice of the Lamb of God. How do I know? I was shown my sinful self, in comparison to His perfection. I know what He has done in my life, I know the relationship I have with Him. Proof? Don’t need it. I know.
I know in my heart of hearts there is a God. The Bible gives us an excellent roadmap to understanding but is not proof.
I come to my belief through the Word and simple logic. As someone else here said, look outside! Look at the universe, DNA, and so many other things we have discovered through science, but we cannot explain how any of them came about fundamentally. None of them.
Anyway, I'm anxious about how you provide "proof" that God does exist.