Einstein developed general relativity in 1915 and published his 'static' cosmology theory in 1917. Hubble didn't discover the expansion of the universe until the late 1920's so there was no possible overlap. Big bang cosmology was developed by Lemaitre, DeSitter and Friedman in the period between 1917 - 1929. Hubble's discovery confirmed the already existing mathematical theory of expanding cosmologies, Hubble was not the 'discoverer' of these cosmologies, however he did provide the conclusive observational evidence supporting them.