Doesn't work that way: there is always an infinite list of possibilities without evidence to the contrary if you allow for a wide enough "solution space" (even if you have already an explanation).
You appear to be claiming that there's an infinite amount of explanations and we can't really know, while also claiming that more data points don't create greater certainty of correlation.
That's contrary to the basis of how science works.
I did not claim the part about more data or that we cannot really know, but rather that if you have to consider any and all explanation in an analysis you have a problem - it's a line of thinking that doesn't help and leaves the realm of science.
For example, is having a simple mechanical explanation for something really evidence against some Devine intervention that is just done so that everything looks "normal"?