The bible makes no attempt to prove the existence of God. Undeniable evidence of God's existence is readily observable worldwide and all of the biblical writers simply assume His existence. For example King David wrote "The heavens declare the glory of God; and the skies proclaim the work of his hands" (Psalm 19:1) Such universal language is readily understood by people all around the world and as far as God is concerned only a morally deficient person would deny His existence and thus David calls such a man a fool (Psalm 14:1)
