It depends on a lot of things that were considered impossible, but not things that are logically incompatible with materialism.
> So, it seems prima facie your claim that immaterial explanations have never been able to adequately answer any question to be incorrect.
No, all the things you point to are material explanations.
The fundamental issue is whether the new theory, materialistic or not, can be quantitatively and empirically tested in some way. I propose the notion of the mind as a halting oracle is such a thing. And we can call it a materialistic halting oracle so we don't violate the need for purely materialistic explanations.
https://am-nat.org/site/halting-oracles-as-intelligent-agent...
No, that strikes me as false. Geometry is very material and can explain a good bunch of mathematics. Differential geometry, an important aspect of modern AI, is necessarily symbolic, but that does not exclude its materialistic applications.
> Even if the entire universe were destroyed, mathematics would still exist.
You presuppose that maths is immaterial to proof that it's immaterial. That stance cannot be argued with, because you cannot show it to be true. If thought seized to exist, there would be nothing left to argue with, so this is reductio ad absurdum either way leading to a false dychotomy. What remains is: "maths" does exist. So my stance holds as much explanatory power as yours, no more, no less, but yours is metaphysical. You idealize things you don't understand, unless you have a concrete plan of action to "Recreate the universe again".
Math itself is necessarily immaterial, and modern science would completely collapse without mathematics.
So, it seems prima facie your claim that immaterial explanations have never been able to adequately answer any question to be incorrect. I see no problem with also proposing an immaterial soul as a scientific hypothesis, if we are able to make the claim quantifiable and empirically testable.