What proof is there that the universe is expanding?

The evidence for the expanding universe comes from a measurement of the light spectrum coming from distant galaxies. The red shift in the light tells us that EVERY galaxy is moving away from every other, in other words expanding. Concurrently, the expansion of space itself, that you are having trouble comprehending, makes sense if you reason it out: At the time of the big bang the Universe took up much less space (it was the size of a tennis ball or so). There used to be less volume (space) in the universe and now there is more, so space is expanding. Not being able to visualize it, while annoying, does not stop it from being true.