I'm guessing it wouldn't take much for Mongolia to become part of the USSR.
So here's my attempt at a slight POD that could lead to some major changes.
March, 1921 the Soviet Red Army crushed the White forces ruling the country. As per OTL, this time they remain.
The Soviet Army remains behind to "help" rebuild the country, and they continent to occupy it, they prop up the Mongolian People's Party and in 1924 following four years of Soviet occupation and the the death of Boghda Khaan and a shamed election later, Mongolia "votes" to join the USSR.