The Proof that God exists is that without Him you couldn't prove anything.
While this proof is valid, no one needs this proof. The Bible teaches us that there are 2 types of people in this world, those who profess the truth of God's existence and those who suppress the truth of God's existence. The options of 'seeking' God, or not believing in God are unavailable. The Bible never attempts to prove the existence of God as it declares that the existence of God is so obvious that we are without excuse for not believing in Him.
Romans 1 vs. 18 - 21 says:
The wrath of God is being revealed from heaven against all the godlessness and wickedness of men who suppress the truth by their wickedness, since what may be known about God is plain to them, because God has made it plain to them. For since the creation of the world God's invisible qualities - his eternal power and divine nature - have been clearly seen, being understood from what has been made, so that men are without excuse. For although they knew God, they neither glorified him as God nor gave thanks to him, but their thinking became futile and their foolish hearts were darkened.
God does not send people to Hell for denying what they do not know, but for sin against the God that they do know.