Unlike those how claim "spiritual knowledge," I can show you how I know and if you have any doubts you can try it yourself. Such as "don't touch the hot stove top, but if you don't believe me, go ahead!"
Proof is a (readily) detectable and repeatable thing, not something only the "endowed" with "eyes" and "ears" can see and hear, but everyone, because we are visible, detectable creatures living in a visible and detectable world.
Now, in the course of our developing civilization, we have come to know that there are things which we cannot see or detect with our natural senses, but need special tools. The discovery of such things shows us that they, even though undetectable to our natural senses, are part of the same physical universe we see around us, and are subject to the same laws as we are, and that the differences are in degree and not in kind. Nothing "supernatural" has been discovered—ever, be it on a microscopic or cosmic scale, so then what justifies assuming that "supernatural" exists?
You write "Suppose you assume that the universe is a gigantic, uncreated, purposeless accident. The question then becomes, what is the evidence for the notion of matter in motion not functioning as it "ought" to function?"
There is no reason or justification to make such an assumption any more than to assume it is created or purposeful, because we don't know, just as no one knows what, if anything happens after this life. I simply recognize that—as of today—we don't know what this is all about with any certainty, that it is a blank page but not necessarily outside our capacity to discover. As for matter, it functions the way it functions, whether we understand why or not.
how claim=who claim
You have just (inadvertently) given a wonderful proof not only of the existence of God, but also of your knowledge of Him, which you try to suppress. If you would like to see it I will show it to you.
Cordially,