Actually, Albert Einstein did not provide direct evidence for the expanding universe. In fact, during his time, the prevailing view was that the universe was static and unchanging. Einstein himself initially incorporated a cosmological constant into his equations of general relativity to maintain a static universe, as he believed that was the correct picture.
However, in the 1920s, the American astronomer Edwin Hubble made important observational discoveries that provided evidence for the expanding universe. Hubble observed that distant galaxies appeared to be moving away from us in all directions, and the farther away a galaxy was, the faster it seemed to be receding. This relationship between the distance and velocity of galaxies became known as Hubble's Law.
Hubble's observations were based on analyzing the light emitted by galaxies and measuring the redshift of their spectral lines. The redshift occurs because the light waves from galaxies get stretched as the universe expands, causing the wavelength of light to become longer, and thus shifting the light towards the red end of the spectrum.
The observed redshift of distant galaxies and Hubble's Law indicated that the universe was not static but rather expanding. This evidence was consistent with the predictions of Einstein's equations of general relativity, which allowed for a dynamic universe. Einstein himself, upon learning of Hubble's findings, acknowledged that removing the cosmological constant from his equations was a mistake and referred to it as his "greatest blunder."
It's important to note that while Einstein's theory of general relativity provided the mathematical framework for understanding the expansion of the universe, it was Hubble's observations and subsequent work by other astronomers and cosmologists that provided the empirical evidence supporting the concept of an expanding universe.