I don't believe that philosophy can prove God, certainly not to someone who wants to disbelieve, any more than it can disprove God's existence. But philosophers still address the question.
Alvin Plantinga is an eminent American philosopher who has long been a champion of an argument that (in summary) goes like this .....
Let us start by assuming there is no God and this natural world is all there is. Then our brains have evolved through natural selection alone. Natural selection works by certain behaviour increasing the probability of survival, which means more of the genes which lead to that behaviour are passed on to the next generation.
Thus, on the assumption we started with, the brain has evolved to choose behaviour that increases our chances of survival, but there is no reason to believe that it has also evolved ways of thinking about more abstract matters that are reliable. Thus our reasoning may be true in some circumstances and false in others, and we cannot trust it.
But it is our reasoning that has suggested the conclusion that no God exists, so the initial assumption is undermined. Plantinga concludes that it is thus irrational to assume a naturalistic belief in the first place.
Of course the argument is criticised by some other philosophers and dismissed by some scientists, but it seems to me to have force. Read a recent discussion of the argument by Plantinga, a discussion of some of the objections, and a discussion of some of the implications.