The invariance of some of our physical "constants" is mainly an assumption.
With Universal Gravitation, Newton postulated that the force which causes an apple to fall is the exact same force which keeps the Moon in its orbit. The planets are kept in their courses by similar forces. Although he postulated the form of this force (F=Gm1m2/r**2), he never measured the gravitational constant, G, itself. When Cavendish measured it a few years later, he did it by observing the acceleration of two lead spheres in a laboratory. If Newton was right about that "universal" stuff, then G as measured in a laboratory here on the earth should be the same G which governs the motions of the planets. Subsequent observations are consistent with that assumption. But it's still an assumption. We have no direct evidence that the local G is identical to the G which rules the motions of, say, the stars in the Clouds of Magellan. Lacking evidence one way or the other, we assume that it is. Furthermore, we assume that it's always been the same as it is now. That assumptions is perhaps less justified, but again it's mostly consistent with observation. If it did change in the past, some odd things would have happened. For one thing, the earth might have changed size. This would in fact be consistent with the old observation that the cratons (the rafts of crustal material which form the continents) can be fit together with no interstitial spaces (that is, no ocean basins) on an earth approximately half the diameter of the modern Earth. That's not actually evidence of anything, so the assumption that the gravitational constant is indeed constant throughout all of space and time is not seriously threatened. Not yet, anyway. There are some anomalies in the structure of the arms of spiral and barred spiral galaxies, and our understanding of Universal Gravitation can't account well for those. There are a few other problems too. But lacking better theories, we've retained the assumption of invariance throughout time and space, parochial though that may turn out to be.
The speed of light is also assumed to be an invariant, although small variations continue to crop up in actual measurements. These are usually dismissed as experimental errors, but that's perhaps a bit glib. If the speed of light has actually changed during the life of the universe, there would be major repercussions. For one, the interpretation of red shift of the spectra of distant objects would need serious revision. Conservation of energy might also need to be reexamined. The idea that a photon retains its energy while traveling for a billion years or so is an assumption - an assumption consistent with some observations, but perhaps not entirely consistent with others.
There are loads of similar assumptions in science, such as the isotropy of space - the idea that the properties of the universe are the same in all directions. Maybe they are, maybe they ain't. Measurements show that they are, but better measurements may show otherwise. We assume that rates of atomic decay are not only time and space invariant, but are independent of outside forces; and again, observation in the main supports those assumptions. For now. The positive atomic charge - the one carried by protons - is assumed to be exactly equal to the negative charge of the electron. This has been measured, to something like one part in ten to the 27th - a very small number, but not necessarily zero. Science is a maze of assumptions, in which we put faith mainly because they're consistent with each other.
Having said all that, I don't put any weight at all on the assertion that the speed of light has changed by a factor of over 20 million in historical times.
