Turing didn't prove anything about human understanding. He proved about computation with an idealized, resource-unlimited computational system, which isn't, at all, the same thing.
Only if you assume unlimited compute time. For instance, if the equations that describe the universe are a million lines long (as opposed to Tegmark's "should fit on a T-shirt" criteria) then it could take an impossibly long time to discover them.
That’s not how scientific discovery works. We aren’t handed a description that might have fractal complexity, but rather we invent models to describe it. Even if reality is infinitely complex, out descriptions need not be. And it’s well established that our approximate models can be vastly simpler than underlying reality.
We have, today, approximate models that are simple. But they're not quite exact for things like quantum gravity. If you want an exact model, it is presumably longer. Presumably, because smart people have looked for a long time for simple models that are more accurate and haven't found one.
If the exact model is only moderately long, then we (or a Turing machine) can discover and simulate it. But it's at least conceivable that the shortest-possible exact description of physics is extremely long.
The issue is more of data availability. Quantum gravity is hard to pin down because the differences are not observable at energies we can test or at cosmic scales we can measure. If we had a probe skirting the event horizon of a black hope the answer might be obvious. But we don’t.
