The philosophy that refuses to believe or accept any premise which is not supported by some sort of evidence, and which therefore maintains that all metaphysical and supernatural phenomena (deism) as well as all theologies and other religious doctrines (theism) are plainly superstitious and, in reality, subject to more sophisticated explanations, or even partly or wholly invalid.
According to adeists (who are essentially empiricists when it comes to the supernatural and the religious) anything can be dismissed which cannot be proven; to quote Christopher Hitchens, ‘That which can be asserted without evidence, can be dismissed without evidence.’
“You may wish to be a deist as my heroes Thomas Jefferson and Thomas Payne were, and you may not wish to abandon the idea that there must be some sort of first or proximate cause, or prime mover of the known and observable world and universe; but even if you can get yourself to that position – which we unbelievers maintain is always subject to better and more perfect and more elegant explanations – even if you can get yourself to that position: all your work is still ahead of you to go from being a deist to a theist. In other words, to someone who says god cares about you, knows who you are, minds what you do, answers your prayers, cares which bits of your penis or clitoris you sew away or have sewn away for you, minds who you go to bed with and in what way, minds what holy days you observe, minds what you eat, minds what positions you use for pleasure: all your work is still ahead of you and lots of luck, because there is nobody, there’s nobody – even Aquinas had to give it up – there’s no one who can move from the first position to the second.”
― Christopher Hitchens
Knowledge Guild 
On the point of what can be known much has been said. The logical mind will determine that if one set of test methodologies works for everything but that which is claimed to exist but aslo cannot be tested, then is it most probable that the claim is false. Certainly there is no test which would show such a claim to be probable and so such a claim resides in the same box with all other claims which are wholly improbable until such time as evidence shows it should not.
To not think like the above requires two sets of tests for reality which are mutually exclusive of one another e.g. faith cannot show us that France exists, nor any other thing that all humans understand to be true. Using two mutually exclusive test methodologies is inconsistent in this way such that when adopting the second you cannot remain logically sound in your belief of the other… or if you can it is not at all clear how.
The existential part of your argument is very comparable to Russell’s Teapot Argument. Please see: https://knowledgeguild.wordpress.com/2013/08/01/russells-teapot/