The Union of Soviet Socialist Republics, shortened as the Soviet Union, was a state that was a union of multiple sub-national Soviet republics. It existed from 1922 to 1991, when it was dissolved. Fifteen independent states emerged after its dissolution, with the Russian Federation assuming the Soviet Union's rights and obligations.
From the end of World War II in 1945, there was a state of political and military tension between the United States and its NATO allies and the Soviet Union and its allies in the Warsaw Pact. This conflict was known as the Cold War, since it never escalated escalated to full scale fighting between the two sides, but there were regional wars, known as proxy wars, which were supported by the two sides.
During the Cold War, there was a nuclear arms race between the United States and the Soviet Union, although no nuclear weapons were ever fired. The closest the Cold War ever came to escalating to full-scale nuclear war was during the Cuban Missile Crisis in 1962.
On October 24, 1962, the Cuban Missile Crisis had been going on for nearly ten days, and many people thought the world would end that week. Colonel Lomax and the retired Lieutenant General Leslie Groves went to Doc Brown's mansion to offer Emmett Brown a large sum of money to invent a time machine, in order to prevent it from ever happening. Emmett Brown showed them his prototype time machine, the temporal field capacitor. After a test, the two men are interested, and Groves informs Emmett that he'll never have to worry about funding again.
After Lomax and Groves left, Emmett had worries that he could be ushering in an arms race through time, coupled with his regrets about ushering in the nuclear arms race of the Cold War through his participation in the Manhattan Project. He had a nightmare that saw Marty McFly travel from 1982, speaking Russian. He dreamed that he went to the future in the DeLorean time machine and saw the Soviet Union and the United States bringing soldiers through time to fight an unending war, as the two sides would always know the outcome and would continue to try to stop it.
After waking up the next day, Doc sent a letter to himself through the temporal field capacitor to August 1, 1962, when he knew that he and his dog Copernicus would be safe asleep in the fireproof lab in Doc's garage. The process of sending the letter so far back in time led to a buildup of flux energy, leading to an electrical fire, destroying Doc Brown's mansion. In the new timeline, the two men never talk to Doc Brown, as they believe him to be an insurance thief.