There were two problems with Einstein's original (1917) cosmological model. The first was what you mention: Einstein assumed the universe was static, but later

There were two problems with Einstein's original (1917) cosmological model. The first was what you mention: Einstein assumed the universe was static, but later observations showed this wasn't true. The second was that his static model turned out to be unstable to either expansion or contraction, something he had forgotten to check.