Working backwards from one of my favorite verses, Hebrews 11:6 -
Hebrews 11:6 (NIV)
6 And without faith it is impossible to please God, because anyone who comes to him must believe that he exists and that he rewards those who earnestly seek him.
Clearly, here, for man's purpose, in regards to God's existence, is to believe that he is and that he is good. From the perspective of man, God's existence is to be that object of faith that pleases God.
My training is to read the Bible as a character study in who God is, and given who God is, what implications that has on man. In this perspective, God's existence is assumed, and the implication is that his existence provides an object for faith. Turning that around, as the question presumes, is linguistically tortured, but still valid.