I agree with your two beliefs.
Symmetry or invariance may be a useful way to see the structure of physical models of the universe. https://en.wikipedia.org/wiki/Symmetry_(physics) I haven't looked at this closely. Relativity is an "invariance" when measuring differences between two events in space-time from any frame of reference. What invariances are there in physical models? Philosophically, what does this tell us about reality?
I have been re-reading Moffat's "Reinventing Gravity". I would like to understand the theory of gravity well enough to make more sense out of Moffat's modification of it. It appears that Einstein's theory of gravity breaks down when discussing galaxies and larger clusters of galaxies. It no longer makes accurate predictions unless one assumes there is dark matter and dark energy present.
Then there is also quantum physics. It is easy to confuse the model with reality here, but one has to know the model to philosophically assess the confusion. These all tie together. I don't think it is possible to compress an atom into a black hole which makes me wonder if black holes are possible. If they are not then Einstein's theory of gravity needs to be modified.
For me, the whole question is philosophical, but I need to understand the mathematics and physical theory to ground that philosophy.