When you say "prove a god's existence," are you speaking of proof though subjective or objective evidence?
I don't personally believe that any evidence for or against the existence of any god can be objective.
Humans are basically driven by selfish concerns. "What's in it for me" appears to be the driving force behind everything they do. Very few people ask what they can do for their god to thank him for their life and for the many ways they can enjoy what he has given them.
For Bible believers, there are so many things in this life that show us Jehovah's generosity, his love and patience. Godless humans think they have killed him off, but he will show the world in a real and physical way just how real he is in the near future if the Bible is correct. His patience has its limits and his purpose in connection with this world is about to come full circle. This is what the Bible teaches.
What makes the difference with the God of the Bible, regardless of how humans interpret his words, motives or actions, is that he leaves all the important decisions to us. He presents us with the details of his purpose in connection with our existence here on Earth....he told us why humans abused their free will at the start.....and what the outcome will be for those who choose to use it wisely and unselfishly in their own lives, as opposed to those who wish to impose their will on others, (as we see all too often today.)
For those who still demand that God show himself physically so as to convince them of his existence, but are unwilling to appreciate the many ways in which he already has, will have no part in his plans for the future. He has no use for selfish people who only want what is good for them. The God of the Bible, through the example of his son, shows us the kind of people he is seeking to populate his kingdom. These are not stubborn, self willed individuals who show no regard for others, but the selfless, humble and obedient ones who will stand up for what is right without raising a finger to harm anyone. They will show themselves to be "no part of this world" in all the ways that count.
I have never seen any god worshipped by men who can prove their existence. So our decisions about worship come from a place that is individual for each one of us. 'Birds of a feather will flock together'.....we just have to choose which "flock" we want to belong to and hope that it is the right one. From God's perspective, whatever we choose is the right one because it tells him who we are and where we belong in his scheme of things. Every single person will be where they have put themselves when the final judgment comes. This is what I believe.