tl;dr- We don't actually believe that the laws of physics are perfectly accurate, precise, or immutable. Instead, we tend to work from the observation that the universe seems consistent with certain models as far as we can tell.
We haven't gotten to explore distant galaxies yet. And given that the observable universe isn't 200-billion light-years wide – it's less than half that in diameter – we really don't have much to work from.
Example: We don't believe that the speed of light is constant
For an extreme example, we often say that the speed of light, $c,$ is a constant – however, scientists don't believe it in an absolute sense. What we actually believe is that the speed of light seems consistent with a constant so far as we have been able to tell.
If we did take the speed of light being constant to be literally and absolutely true, it'd imply stuff about how smooth spacetime must be and answer structural questions about scales at-and-below the Planck length. Unfortunately, science isn't that easy; 'til we can meaningfully test how fast light moves between two points ${10}^{-100}\,\mathrm{m}$ apart, if such a test is even physically sensible, we can't claim light to move at a constant rate at that scale.
The speed of light is an extreme example since its constancy is such a cornerstone of modern physics. The point's that we don't generally assume even the most cherished scientific assertions to be absolute; it's all about accepting the apparent consistency of an explanation in its correspondence to observation until we have a new explanation that corresponds better, applies more widely, is easier to work with, or/and has some other merit that makes it worthwhile.
We don't believe the laws of physics are the same in other galaxies
We don't believe that the known laws of physics behave exactly the same way in other galaxies. Instead, what we've got are a bunch of models that seem to work better than any known alternative in the contexts in which we've tried to develop them. 781
So if we must speculate about how things work in a far-flung context, the best we can really do is tentatively extrapolate until experimental verification can provide us with more insight.
So, maybe the fine-structure constant, $\alpha$ varies over the universe; perhaps we'd one day describe some sort of universe-scale physics that causes it to vary. But, 'til we have some mechanism to describe it, what can we really do?
Historical analog: Atomic physics
In the early 1900's, scientists were working with trying to model the atom. Their early attempts were largely based in the physics that they already knew from human-scale physics, e.g. the <PERSON> model and <PERSON> model for atoms. They basically tried to force observations into the framework that they already knew, then relaxed the framework as that didn't quite work.
Exploration of the distant universe may work out similarly. This is, we'd likely try to fit everything into the models that we've got, then relax them as necessary to capture observations that we can't make fit into existing models.
Of course, this doesn't mean that we believe or disbelieve in our current models applying. It's just that, until we have cause to suspect otherwise, we tend to suspect that our current models are more likely to be useful than models that we have no reason to suspect to be useful, e.g. random speculation. 484