There's no empirical proof that Earth is in fact moving, there's only a model of the universe that "explains better" the empirical data we have about movements of planets and stars.
But nothing prevents this data we have from being explained in terms of a static Earth.
I am on the earth. I can dig a hole and move the earth. The earth is made of atoms. Atoms are never still. When I dig my hole, I am moving atoms left, right, up, and down.
no one can state that the Earth is moving, for the same reason no one could state that it was static in the past, or that no one could state that the Sun is static today, or that our galaxy has a static center.
If Earth were not moving, the vast majority of matter would be moving faster than c. According to our current understanding of the universe, this is impossible.
If c designates the velocity of light (relative to the ether), then its velocity relative to the earth should be c-v for a light beam moving in the same direction as the earth, and c+v when it moves in the opposite direction.
Experiments have shown that c+v and c-v are equal, so v must be 0.