And they have failed. Even Immanuel Kant.
If God is transcendent (as Christian God is, although He makes Himself knowable), then trying to deduce his existence from the phenomena using formal logic would eventually run into a wall that is incompleteness theorem(s). That's what faith is for - to take lead in the regions where reason begins to fail.
Kant did not prove God existed, on the contrary, he wanted to prove we could not prove, nor disprove, God exists. He wanted to clear out reason to make room for faith.