The cognitive fact that you "know of physical existence" does not itself exist. And yet this bias for physicality is so strong that you just can't acknowledge that 'physicality' is, itself, an idea that does not physically exist.
Everything that "exists", exists as an idea in our minds. As a 'cognitive conception' generated by sensory input and cognitive processing. Existence, itself, is a cognitive conception. Perception IS conception. Neither happens without the other happening. And it ALL exists.
Sherlock Holmes and gravity both exist. One is man-made and the other is not. One is experienced through imagination while the other is experienced through the body and through circumstance (memory). Those different methods of experience and cognition do not define, nor negate existence. Ideas exist, circumstances exist, values exist, and mysteries exist. As surely as gravity exists.
Let's analyze the term "reliable". What does it mean for something to be "reliable"? And what is the criteria for determining this reliability? Why is reliability so important to you? Is it the quality of being predictable? Why would that matter? It it about control?
The reason I ask is that a lot of your fellow humans are not as concerned with existence being reliable and predictable. They aren't trying to 'figure it out'. They aren't obsessing over "physical evidence" looking for the trth of it all. They're just trying to survive and be happy. And maybe create some sense of meaning and purpose for themselves.
Feeling good IS IT'S OWN TRUTH. In much the same way as doing good is it's own value. These require no "evidence" to be true. They simply are their own truth.
How about just BEING HERE and letting it all be the truth. Without the evidential analysis and presumptions of validation and invalidation. How about we just let good be good for it's own sake. And joy be joy, and God be God; without all the doubt and judgment and obsession with the physics and predictability of it. Believe it or not people all over the world are already living this way and they're fine with it. They don't need mathematics to tell them it's OK. And they don't need to understand God to rejoice in the divine benevolence of being alive and being human. They can just let the miracle of it all be what it is.
But not the atheist. Ain't gonna be no damn miracles in HIS universe! Just mindless physics. That's IT! And he's gonna figure out how it all works so he can predictably control EVERYTHING! Science gonna make him GOD!