God proves it not man. Is that statement difficult for you or something?
My problem with it is that it is a meaningless statement to say that "God has the burden to prove God's existence", and your support for this seems to merely be, "God's existence is obvious or self-apparent". Now, the latter, for whatever reason, cannot be true according to the meaning of the word "obvious". Usually people revert back to "God of the gaps" arguments (e.g., since we don't know how life comes from non-life, God must be the explanation), but you haven't even gotten that far.
You seem to be claiming:
1. Belief comes from grace. (can you support this without resorting to other claims in scripture?)
2. Grace comes from God. (can you support this without resorting to other claims in scripture?)
3. Therefore, belief in God would not exist unless God exists. (this is only true if your premise is assumed, and part of this would be assuming that God exists and is the source of Grace.)
Therefore, you haven't provided any reasoning that doesn't utilize logical fallacies. I would like to understand why you are so confident in your claim here, but circular logic and/or arguments from ignorance don't help with that.