There are theories that Stalin always knew a war was coming and was preparing for an offensive attack. There are also contradicting theories that Stalin ignored field and Soviet/ British intelligence reports on German preparations and did nothing. In either case, there is no excuse for the Russians to be unprepared.
RKKA wasn't fully mobilised until winter 1941. Wehrmacht on the other hand was fully mobilised and full of veteran soldiers since day one. Germans didn't even have any plans for additional conscription until the Battle of Moscow, which played a part in their demise later on. By the time Soviet Union gained quantity advantage it already lost most of its modern equipment, about a third of its recruitable population and a big chunk of industry. During the first stages of Barbarossa Russians simply didn't have enough men at the front to use all the equipment they had, their tanks were left without supplies because there wasn't enough people to drive the trucks with shells and fuel. About half a million mobilised Soviet soldiers were encircled while still on the way to their divisions. There wasn't much they could do even if they had enough officers, which they didn't due to NKVD supremacy over army. Regardless of how much at fault Stalin is here, you can fix both in the game.
Worse, he had surrounded himself with obedient cronies who towed his line and even though there were Russian officers who wanted to adjust their tactics based on the Blitzkrieg in France, their voices were drowned out.
G. K. Zhukov was a Deep Battle proponent and used mobile warfare and overwhelming power tactics at Khalkhin Gol a few months before German Blitzkrieg in Europe. He didn't have enough infulence until well into the war but it isn't a concern for a player.
I think we need to give a lot more credit to German tactics and strategy for their victories.
I may agree on tactics but the German strategy was exactly that. Defeat the enemy before they can do anything. There was no comprehensive theory for strategic bombings, logistics, troops and pilots rotation, industrial and R&D goals. Third Reich had a lot of skilled people who knew what they were doing but startegic thinking wasn't their strongest point.
Similarly, the Russians had more tanks, planes and artillery. Although these were of lower quality they were numerous enough to have dented the German advance, had it not been for superior German tactics.
The most numerous tank Wehrmacht operated during first months of war with the Soviet Union was PzII which is also when they made their significant gains. In Ukraine some encirclements were done by WWI style cavalry troops without air superiority in the region. Their early success had nothing to do with quality of German equipment, if anything only their fighter planes were significantly better in 1941. Soviet troops were just overran by large autonomous mobile divisions. It was a novelty available only for armies with great number of good officers but it could hardly be used without quantity superiority at the front.
So the point is that the first few years of WWII were all about tactics, where the Germans excelled. Once the Allies and the Soviets developed their own tactics to counter the Germans, it was just a matter of out-producing them industrially.
Deep Battle field manuals used in Soviet offensives of 1942-1945 were released in mid-30s. There are requirments an army has to meet in order to execute their plans. For Soviets it was quantity superiority that was needed to deny the enemy mobility and trust between HQ and army group commanders because the latter had to act on their own in order to reach operational goals. They had neither and found themselves in the worst possible situation for their doctrine during the first months of war.