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They didn't have much time, they (Bolsheviks) came up with the Holocaust narrative when Germans exposed the Katyn massacre. Bolsheviks claimed that Katyn was perpetrated by Germans. When the red army began reoccupying Eastern Europe in 1943-1945, they did what they accused Germans of doing: they massacred locals, just like they did at Katyn, and blamed it on Germans.
Bolsheviks then tried to use these massacres, including Katyn, to prosecute Germans for war crimes, and only due to gigantic effort from the Brits and Americans did they drop Katyn, because it was very obvious that Bolsheviks did it. They kept all the other fake war crimes though.

Bolsheviks were also conducting the war with a full preemptive destruction of the area they were attacking, even if the area was undefended. They killed a lot of civilians when they destroyed concentration camps. These camps were holding ethnicities that were deemed to be a potential fifth column, like Japanese in America. The problem here is that Allies were advancing from the West, and they discovered concentration camps too. There were independent journalists, and Allied soldiers were of higher moral stock than the Russian soldiers, so Allies just reported the truth: concentration camps were regular, but the prisoners were underfed and untreated for sicknesses. Bolsheviks then had to come up with a justification pretty much on the spot, so they claimed that Germans were systematically killing Jews in industrial-scale facilities. Otherwise, if Bolsheviks reported the truth, it would become apparent that Germans weren't mass killing people in Katyn-style massacres. Look up the map of the concentration camps: 100% of the concentration camps "liberated" by the Bolsheviks were "killing camps" where Holocaust allegedly happened, while 0% of the concentration camps "liberated" by the Allies were "killing camps".

Bolshevik story alleging industrial killing of Jews was incongruent with Bolshevik story alleging Katyn-style mass killings, where people were killed with bullets and buried in mass graves. Therefore, Bolsheviks came up with the story that Germans were psychopathic torturers, and that Germans just enjoyed killing Jews with whimsical contractions and for weird stuff. Electrified floor, human skin lampshades, human soap, gas chambers disguised as showers, and whatever else the Bolshevik mind could conjure up. Importantly, it was accepted by the Allies, because they allegedly went to war to keep Poland independent, but as a result of the war Poland became occupied by Bolsheviks. Allies then had to sell it to the populace by portraying Germans as evil. With time, the most obvious stuff about Holocaust has been discarded, and now the only one left is gas chambers. It is retarded too, but it cannot be allowed to be disproven, because it's the last and only part of the Holocaust narrative.

And by the way, in 1990s, Soviet archives were opened, showing that there were more internal documentation about Katyn massacre in the Soviet Union, than there were about Holocaust in Nazi Germany. One massacre was better documented compared to an operation costing billions, executed during the biggest war in human history.