What is left when you eliminate everything with a name?
We know God by unknowing, by a manner of uniting with God that exceeds the compass of our minds, when the mind recedes from all things and then leaves even itself and is united with the super-resplendent rays of the Divinity…
(Saint) Thomas Aquinas
We have names for those things which exist in our form of life: water, cups, mountains, clouds, friends, strangers. Now consider this: what is left when you eliminate everything for which we have a name?
This is the essence of what is called Apophatic theology – this is, if you can name an attribute of God, you're not talking about God. So, in a manner of speaking, God is whatever is left when you eliminate everything with a name.
Now, if you take that to be the definition of God (a so-called negative definition), then by definition God must exist. This might not be the old bearded man in the clouds version you grew up hearing about, but face it, you didn't really believe in that anyway, did you?