I would agree with many of your points, but: Do not mix up a mathematical proof with a "proof" in general science. ;)
A mathematical proof says something is or is not. There is no doubt (if we accept some axioms). In general "proofs" (better: validation) of theories describing nature can only say, something seems likely or unlikely (and to what extend). To be more specific: One formulates a hypothesis and a null hypothesis (often saying the effect described in the hypothesis is non-existent) and then look at the data and say whether one can show the null hypothesis to be highly unlikely. Your are not saying your hypothesis is right, your just saying the null hypothesis is likely wrong and your hypothesis _could_ explain why.
To support your claim: As we can we only say what likely is wrong, any theory has to be falsifiable. Everything else is not science. I can't say: "My god is out of reach of man and their tools, he can't be perceived or measured, neither it's actions. And science hasn't proven me wrong about it's existence, so it must exist." and expect science to take me serious, as it is impossible to (in)validate this claim with tools of science.
To the general topic: I have no problem of people being religious in general (as long those don't rub it under my nose all the time, play missionary or try to use it for their advantage), but there is a big misunderstanding about science, what it can achieve and how it works. On both ends. How often have I read post saying science is just another kind of religion. No it's not. Maybe some pseudo sciences make non-invalidatable claims, but definitely not natural sciences and mathematics. On the other hand people trying science to disprove religious believe will not succeed, for reasons mentioned above. The only thing you could do imho is to argue, why you consider it not reasonable to have religious believe.