What I am saying is that the Bible does not even attempt to "prove" the existence of God. It is taken as fact.
There are various places where "demonstration" is provided even where "proof" in the empirical sense has not been offered. For example, we have the polemic against idolatry in the second section of Isaiah. God undertakes to prove Himself as true and trustworthy in comparison to the gods of the nations. One fact in particular, fulfilled prophecy, is given as an argument for believing He is God and there is none other.
True. I guess I see your point. I think my statement is still true. The Bible does not attempt to prove the existence of God. However, there were men in Scripture who set out to prove that the one true God was the God of the Bible. For example, Elijah on Mount Carmel. As I read the OP, that seems to be what he is asking: not to prove the existence of God but the God of the Bible. There is no need to prove that there is a God, it is clear from nature and from the Scriptures.
1 Kings 18:24
"And call ye on the name of your gods, and I will call on the name of the LORD: and the God that answereth by fire, let him be God. And all the people answered and said, It is well spoken."