Science can't "prove the existence of God" in principle. Plus the "basic mode" of God (if I can call it that) is not existence at all: It is perfect Being. That is what is indicated by God's self-revealed Name: I AM THAT AM.
Philosophically speaking, Being and Existence are not the same thing.
Plato gives us another way to think about it. God is utterly transcendent, utterly "Beyond" the immanent world (i.e., the universe). As such, He can never be an "object" of direct or indirect observation, and thus cannot in principle be accessed by the methods of science.
So naturally, I don't expect "science" to prove anything about God at all. Certainly, I don't need it to.
You certainly would not want to accept any scientific findings relating to God, especially if those findings somehow disagreed with your own religious faith, would you?
See the statement above.
Then what exactly is your problem with it?