The Bible does not try to prove the existence of God. It simply presupposes it. The existence of God is not dependent upon our belief. God either exists, or He does not. You can neither prove, nor disprove the existence of God.
Whether or not we believe in God depends upon our response to the evidence we have been given. Romans 1 tells us that God has given us ALL the information we need to believe that God exists from the created universe (General Revelation).
So why then do people reject the idea of God? The problem is NOT that they don’t have enough evidence, the problem is that their hearts are hard and they do not want to submit to God’s rule and authority in their lives. This is the main problem with the skeptic. He is not unconvinced primarily because of his mind, but rather his will is in rebellion.
Moving someone from the position of Hard Atheist, to Strong Agnostic is useful because it essentially removes an element of stubbornness, and puts the conversation on a more humble footing, where it belongs. The decision to accept the existence of God is not based on Omniscient knowledge, but rather on reasonable certainty, based on the evidence God has provided.