The New Testament has an interesting truth-claim in this regard.
Romans 1:18-20 For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who by their unrighteousness suppress the truth. (19) For what can be known about God is plain to them, because God has shown it to them. (20) For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse.
So then, according to the Bible, the proof is all around us and we have been created with the ability to perceive and understand. That makes the denial of the evidence God put before us an intentional (or at least chargeable) act of our own.
It's totally understandable that Christians use the Bible as the primary source document for the proof of or reference to God existing. However, how is that different than saying reincarnation exists because Buddhist texts say that it does? Or to give a current secular analogy: Saying that Darth Vader exists because Star Wars clearly says that he does.