After winning the Civil War in 1921, Lenin had established a Communist dictatorship in Russia:

Communist party membership rose to 700,000 in 1921
All government power was in the hands of party members
All opposition had been purged out of sight
March 1921: Lenin announced an end to factionalism within the party

Further, when the Civil War was over the Bolsheviks took control of many parts of the former Russian Empire. These were then organised into socialist republics, with the main body of governance from Moscow.

1923: Lenin organises the four republics; Russia, Byelorussia, Transcaucasia and the Ukraine into a united state
This state was called the Union of Soviet Socialist Republics (USSR)
1924: The USSR agreed on a ruling constitution
One party was permitted in this united state - the Communist Party

Lenin: Economy and Society