If all matter after the Big Bang moves away from each other wouldn’t the center of the universe be totally empty and wouldn’t the universe be like an egg shell with all the galaxies concentrated in the shell?
The Big Bang is not an Explosion
This is a common misconception because the analogy we are given about the Big Bang is that of an explosion where matter of course starts in the center and then moves out to the edges. However that is not a good analogy for what happens.
Instead imagine the universe and the matter in it as dots on an inflatable balloon. Does the surface of the balloon have a centre?
It does not and as you inflate the balloon the dots get farther apart but there is no “central” location getting empty.
Likewise our universe is getting inflated causing stars and galaxies to move further apart from us but only because space itself is getting stretched.
Hence regardless of where you are in the universe it will look as if everything is moving alway from you.