Noether’s Theorem merely shows that the maths works for the maths. It doesn’t prove that the maths tells us anything about reality. That is simply a matter of faith. The clue is in the word “theorem”. None of the practicing scientists I have worked with it have professed that faith, although I have heard it from high school level science teachers.
The only axioms it requires are the ones required to do calculus. That's it. If you think calculus works, then this works. (Mostly because Lagrangians are just systems of differential equations.)
And the point is there is no way to prove that Physical laws are not derived by pure luck - “luck” meaning something we don’t understand and haven’t thought of.
Solipsism is not a particularly productive or useful philosophical approach.
But even if you treat Noether's Theorem as a proof, it is possible that aliens on a distant planet might derive mathematics that is equivalent to our own, but looks very different, in the same way that the World Tree looks different to the Great Wheel.
It is not possible that they could derive mathematics
that also work but which deny Noether's theorem. Your insistence on the total absence of any form of knowledge does you a disservice.
If they develop something that is of equivalent descriptive power to calculus, they
will derive their equivalent of Noether's theorem. It is not
logically possible for them to develop something that can do what calculus does and somehow disprove Noether's theorem. It is one of the most fundamental, bedrock parts of mathematical physics--and it is a mathematical proof. All you need to do is observe a symmetry in nature to find the conservation law. E.g. the fact that physics works the same at time t0 and different time t1
requires that energy is conserved. (And, importantly, if it
isn't conserved, the theorem also proves that there
must be some kind of damping effect.)
The human brain was not designed to comprehend the universe, it is pure hubris to suppose it is capable of doing so, any more than the brain of any other animal is. That’s why so many scientists have said variants on:
“The Universe Is Not Only Queerer Than We Suppose, But Queerer Than We Can Suppose”
Frankly? I don't trust most scientists to say a damned thing about
philosophy, which is what they're doing here; that's not a
physical claim, it's a metaphysical one. Mostly because--from experience, as someone who actually
has studied both--most hard-science scientists couldn't philosophize their way out of a paper bag
with the bottom cut out. What passes for "philosophy" amongst most physicists, biologists, and chemists rarely rises to the level of an introductory freshman course.