By natural causes do you mean ''anything but anything which a religious person could point to and draw correctness from''?
The point about natural causes, and science's foundation in philosophical naturalism, is that the data should be the same regardless of who measures it. On that basis, no, it should be something that anyone, religious or otherwise, can point to and draw correctness from. Some of them choose not to, of course, some of them try to twist selective parts of the data to fit their pre-conceived agenda (and that's some on both sides), but the tools are there to identify and correct that.
Has natural causes all the way down been proven? is natural causes all the way down based on mere extrapolation or is it from a desire for that to be so?
Natural causes all the way down is the presumption of philosophical naturalism - it's less 'proven' than the rest of science that rests upon it. What it is, partially, is validated by the continued success of science at explaining phenomena in a coherent way, and then from those explanation hypothesising on possible consequences which can then be validated or disproven by further experiments. The longer and broader the body of evidence behind our 'scientific knowledge' becomes, the better we can trust the presumption of natural causes all the way.
Natural causes all the way down is a bit suspect since there is the presence of intelligence and even darwinianly unevolved intelligence and because we have no way of knowing whether the naturalist narrative is ever comprehensive.
I'm sorry, I've had three runs at that, and I'm still not sure I get what you're saying - if, as I think it might be, you're suggesting that there is evidence of an underlying intelligence 'behind' the universe then I'm afraid I don't see it, and neither does the majority of the scientific community. All the various intelligent design arguments have been thoroughly debunked.
It's true, we don't at the moment know whether our understanding of the naturalist narrative is complete, and we don't know that we'll ever know, or even if it's possible for humanity to completely understand.
However, those grey areas beyond our understanding, the 'gaps' have been shrinking for a long time, and there's no immediate reason to think that they'll stop any time soon.
O.