That's not the definition of Christianity. Catholicism has a long philosophical tradition discussing the existence of God, and that tradition is far from refuted.
Mathematical proofs need no physical evidence. They're saying something similar is accepted by some Christians. That's an internally consistent viewpoint. Us skeptics simply misunderstand their irrefutable logical proof.
You appear to be shadowboxing an argument where no arguments were made. If anything in my observational comment strikes you as remotely controversial or contradictory to yours, something has gone awry.
Well, there are some atheists that argue that God's omnibenevolence is incompatible with the evils in the world, meaning God cannot exist (or at least, is either not omnibenevolent or not omnipotent, and if these are part of the definition of God, then God insofar as the term refers to something with at least these two properties, does not exist). Theists have responses to this argument, but the point is that the subject matter is something that can be rationally discussed.
Sure, I've engaged in similar discussions in philosophy classes, but this was always about whether a specific definition of "god" could exist and lead to discussion like "can God make a rock so heavy even they can't lift it".
It never has lead to a point that proves God exists or not. Unless philosophy has moved way beyond my readings and I missed it.
There are no physical proofs available that Christian it is right. As I say, it is all based on faith and belief.
Several other religions also have long philosophical traditions that are equally plausible - or not - and for which no physical proof exists.