There's a more basic question: How do we know the galaxies are moving? It seems (I haven't seen any other response, like... ever) that we have one and only one way to measure the speed of galaxies: the red shift.

It's impossible to triangulate those huge distances and the time scale would also be a barrier, so no way of confirming the red shift calculations with a different method. That means that if the red shift was caused by any other effect, say the light "degrading" after millions of years of travelling the void, all the calculations would be invalid.

I've asked about this many times and the answers are in the line of "we don't know any other reason for the light to red shift" and "the current theoretical frame is consistent", even if there isn't any other measure to be consistent with.

There was a prediction (expansion is related to Big Bang) that the far away galaxies, being younger, would have a different composition. This prediction seems to be failing, but advances in instrumental could give us a more precise answer in the future.