What proof do scientists have that the universe is expanding?
We have proof because very distant galaxies appear as redshifts. A redshift is a change in color when an object that emits light is moving away from the observer. It is called a redshift because it "shifts" to the "red" part of the spectrum (which has the lowest energy)
Galaxies are moving away from us in every direction, so we know that at one time the universe was smaller. Simply go back far enough, and the universe would have been contained in something the size of an atom; what we call the Primordial Atom.