This is a very common question – if just a few more things had gone Germany’s way, could they have pulled it off?
The most important thing to understand about the way Barbarossa played out is that almost everything was already going Germany’s way. What actually happened in our timeline was like the Wehrmacht rolling two dice and getting an 11. There’s very little additional “good luck” that could be had within reason.
So when you ask is this doable:
What is actually being asked is “could the Wehrmacht move enough men and supplies across Russia to defeat the Soviet divisions opposing them.” It’s helpful to think of warfare on this scale as quantities rather than individual men fighting individual battles.
It “costs” a certain amount of your men and material to destroy a certain amount of enemy men and material. And unfortunately for them, the Wehrmacht simply didn’t have those resources available. If you look at the first 5 months of Barbarossa or even the battle of France, for the Wehrmacht paid 1 casualty for every 2 it inflicted.
The capture of 4 million enemy soldiers in those two time frames is why they are seen as amazing victories; but even in those campaigns which create this mythical status of the blitzkrieg, it cost a lot of German blood. (And they lost plenty of vehicles too.)
There is no real way to get enough fuel and production in place by June 1941 to allow Barbarossa to fully destroy the Soviet military as a battlefield force by the end of the year, even if the casualties were not an issue. And by the summer offensive in 1942 (operation blue) the Soviets were able to produce and supply enough men that Germany would never be able to defeat them, much less build up enough for a successful major offensive.
Notice how German production (in this chart in tanks and SPGs, but it’s broadly true for all types of output) only peaks in 1944. In 1941 they don’t have enough output to fight a war of attrition.
The staff that planned Barbarossa thought the Soviets had 150 divisions and destroying most of them would cause a surrender. In reality, the Soviets already had 300 divisions in the field, three quarters of them in the west, and would swell greatly within a year.
Maybe if Hitler diverted resources from the Mediterranean – most of the Luftwaffe’s heavy bombers and their precious aviation fuel were tied up there – there would have been more resources available at Moscow. But there were over a million defenders of Moscow.
Even if it didn’t turn into Stalingrad, and the Germans could fight as advantageously as they had through Ukraine and Belarus, army group center would have to bleed ~600,000 casualties to take Moscow.
And that gets you through Moscow, and the front merely shifts. It’s another 1,000 miles to the Urals. (Not to mention Leningrad, and the Caucasus, and the rest of the several thousand mile front.) Of course, the luck starts running out by mid 1942.
In order for Barbarossa to succeed as it was launched, or at least the general war against the Soviets to succeed, the Soviets would need to make more mistakes than they actually did. “Our enemy will remain stupid” is not something to be relied on. And we know from the real history that Stalin wasn’t going to break and just give up.
The major issue is Germany is fighting most of the world at the same time so their resource base is very finite. There are no good ways to resolve that in 1941; you’d have to go several years earlier and radically change how the war went from the outset.
