Wikipedia says that Einstein was visiting the USA when Hitler came to power in Germany, which made him decide to stay instead of returning, as he had realized life as a Jew would be rather inconvenient under the NSDAP. What if he does not visit the USA, and instead once the Hitler comes to power, he decides to go to the USSR?
He was a socialist and thought highly of Lenin, so it seems within the realm of possibility that he would chose the USSR, which is also closer. Maybe the NKVD offers to smuggle him in. So what happens next?