Perhaps we agree that your position implies that we never have any real evidence for one thing over another. We do not agree that in fact we never have any real evidence for one thing over another, and I don't believe you actually live as if you never have any real evidence for one thing over another.

In any case, if your position leads you to this sort of cognitive nihilism, so much the worse for it.

We have plenty of plausible explanations for abiogenesis. We don't know whether any particular one of them is right -- good evidence about what happened billions of years ago can be scarce. (Not because of any general impossibility in getting evidence about the past. Sometimes it's there, sometimes not.) And we for sure don't know all the details. Maybe we never will.

That isn't any sort of advantage for creationism as a theory of the origins of life, because we also don't have any details of how God allegedly created life. "God said 'let there be X' and there was X" is no more detailed an explanation than even the handwaviest naturalistic theories of abiogenesis.

(We should ask: how detailed an explanation should we expect to be able to figure out, if either sort of theory is right? And I think the right answer is "probably not very detailed in either case, though the prospects are maybe better for the naturalistic theories".)

I understand that you're saying that divine intervention could produce non-differentiable changes. But I think you're completely wrong about the logical relationships between different kinds of change and possible divine intervention. (1) I'm pretty sure that as far as human observation can distinguish, anything that can be done by a non-differentiable divine intervention can also be done by a differentiable one. (If you restrict God to real-analytic interventions, that might be a different matter.) (2) I can't see any reason why non-differentiable changes should require any sort of god; I already gave several examples of (conjectural but) perfectly respectable naturalistic physics involving non-differentiable changes.

When you're faced with something that doesn't fit well with existing physical theories, you can postulate divine intervention, or postulate that some amended naturalistic theory might fix it up, and that's true whether or not something nondifferentiable seems to be involved. (Especially as, lacking the ability to look infinitely closely at things, we can never tell for sure whether something nondifferentiable is going on. E.g., one of my examples of possible nondifferentiable change in naturalistic physics was "wavefunction collapse", but you could have objective wavefunction collapsing that happens smoothly but very very quickly and no observation we're currently able to make could tell the difference.)

Historically, the track record of the "look for amended naturalistic theories" approach is pretty good; it seems like it leads to genuinely new and improved understanding more than the "give up on naturalistic explanations and say a god did it" approach does. And there's an obvious reason why: if you just say "God did it" then that doesn't make any progress in understanding, whereas if you make yourself look for better naturalistic theories that actually work then you're forced to come up with theories that do a better explanatory job. In principle, of course, it might happen that every time you postulate "God did it" you get new insights into the purposes and preferences of God, and that might e.g. help you make predictions just as well as new scientific theories do. In practice, that doesn't actually seem to happen. (One might ask why that is, and of course the atheist has an obvious answer to that question.)

So, e.g., let's take your example of gravity and the rotation of galaxies. We don't yet know what's going on. We have a rather vague candidate naturalistic explanation: there's a load of stuff in the universe that has mass but doesn't otherwise interact much with the things we can detect. That isn't a very satisfactory explanation because it's so unspecific (though e.g. it does let us make sense of some puzzling things besides the rotation of galaxies, such as the so-called "Bullet Cluster"). You suggest that maybe it's "God working exerting a differentiable influence". Could be.

So, what might be our state of understanding 50-100 years down the line? We might be just as confused as we are now. But it seems at least plausible that we might by then have a better naturalistic theory (more details, more concrete predictions, more things we can check), which may or may not still involve "dark matter". Do you think it's plausible that we will have a better divine-intervention theory? One where we can say "we now understand that the rotation of galaxies is the way it is, because God is doing X, which he wants because of Y"? So far as I know, the number of cases where this sort of intellectual progress has come out of saying "God did it" is zero.

That doesn't necessarily mean "God did it" is false. Maybe we're unlucky (at least in so far as we were hoping to understand the universe) and a lot of things are the result of divine activity that's simply beyond human comprehension. But every time we see something puzzling, go looking for naturalistic explanations, and find them, that becomes less plausible.