WAIT, I have it.
The Soviet Union rolls over Poland, winning a battle of Warsaw. This emboldens the far left in Germany, which now neighbors the Soviet Union. Lenin lives a little longer, long enough to see Joseph Stalin stripped of all power--making Leon Trotsky the next leader of the Soviet Union.
The Soviets grab Hungary (Bela Kun) and crush Poland. When the Great Depression breaks out, a heavily Bolstered KPD comes to power in Germany, while Nationalist elements are crushed in Spain. The real action, however, is in China, where Japan and the Soviet Union fight a prolonged war for control.
With the resources to bear and stuck in a decade-long conflict against Japan, the Soviet Union researches weapons technology with the support of Communist Germany. Among these technologies is the Atomic bomb--the rest of Europe is squabbling but slowly recovering from the Great Depression. In 1962, the Soviet Union tests a nuclear weapon--many other countries could have been first, but neglected the investment.