Albert Einstein showed in one of his papers in 1905 that Brownian motion could be explained by assuming that matter is made up of tiny particles. His paper predicted how the motion should look like and also allowed for the calculation of the mass of a single molecule. Current evidence includes: 1. Individual ions (atoms with an electric charge) can be manipulated using electric and magnetic fields. 2. Elevation maps can now be made that show bumps caused by individual atoms.
Atoms are incredibly small and we cannot see them, even with very powerful microscopes. If we cannot see them, then how do we know they are there?