Barbarossa as conceived had an element of futility build into it, but on the other hand there are instances were Germany could have performed better, resulting less strain on the Germans which results in less opposition and so onward. Considering how close they got OTL it should be possible to get a little further, a little easier (not a lot further, because of logistics).
My favorite POD would be that they continue their drive on Leningrad rather than pausing in July, perhaps reinforced from the air and take Leningrad on the march coinciding with the OTL Finish offense.
What is your POD?
What’s your take on 1942 in this scenario?
Well, that certainly makes it easier.
However, there is a few more suggestions:
Quicker resolution in Greece so AGC has its panzers ready in time. Butterflies the diversion of AGC.
Quicker decision to end the BoB and maintain the Blitz as a smaller diversion (3000 planes and air crews lost at a time when Barbarossa was the strategic prize).
There's a fundamental misconception. More stuff doesn't always help, they can't supply the stuff they have, and the stuff they have is suffering attrition at a rate that means they cannot sustain the kind of forward motion you require. In terms of destroying Red army formations when they met them the Axis forces was already massively successful, but that is fundamentally not the right measure of success i.e Barbarossa didn't fail because the Axis struggled to kill the Red army when they met it*.
Taking Leningrad "on the march" without a protracted siege? It's a city of 2m people if it resists (and it will) you will need a huge force to take it without wearing it down first. And you still have the usual issues the German army is two armies, one panzer army that while fast is the minority of forces and brittle when not on the move. The second and the the majority overall are infantry that have to walk. Panzers can't take and hold a city (wrong force mix and not enough men). So to storm and hold Leningrad on the march you will need to somehow get enough infantry divisions there and in shape to do it and in time to follow your Panzer spear thrust into the city. This will mean either slowing your panzers down or parking them while they wait for the infantry to catch up , or somehow mechanizing a score of infantry Divs (and supplying that).
There's also a couple of questions about "My favorite POD would be that they continue their drive on Leningrad rather than pausing in July"
But they had to pause because they were advancing into huge area and had be forced spread their forces out**. Leib felt he needed 35 not 26 divs to avoid this so where do they come from how do you support them etc, etc. And that's just in order not to pause, we're not even talking about getting to, concentrating on and then taking Leningrad on the march.
Moscow same problem but further and approximately 2-3x bigger once they get there!
Rostov on Don is at least smaller than Leningrad and closer to the Axis starting point than Moscow.
But you want to do all this at the same time so you are still splitting your forces and having to sustain three advances with all the issues that entails.
On top of that you also have the fundamental difficulties that the Germans both underestimated the size of the Red army in June 1941, got were it was wrong, and massively underestimated the Red armies ability to mobilise reserves quickly and in huge numbers. Even if they have perfect intel on these three things it doesn't actaully help them because they will still have to deal with the reality of them.
The other big point to make is the German plan was not to beat the USSR by reaching points on a map it was to defeat the red army.
So for the axis to bum rush the USSR like this (and that is what we're talking about), you will need significantly more forces, which means you will need vastly more support for them in terms of resources and logistics (since they couldn't support the OTL advance as is even at the slower rate than what you are suggesting).
Forget freeing up some tanks from Greece a few weeks earlier or cutting BoB short to save some planes. You need something like not attacking western Europe first and concentrating solely on building up forces for a considerably larger Barbarossa and somehow working out how you can both man an invasion both larger than OTL Barbarossa, disproportionately better supported and resourced than OTL Barbarossa and more successful than OTL Barbarossa. Which remember couldn't even advance simultaneously on three fronts after a couple of months let alone reach and seize these cities all in six months. Remembering it's not just the manpower in the combat units and logistics formations but in the factories etc
But even then I'm not even sure Germany even on it's Jan 1940 borders and Nazi run economy concentrating solely on this can do this. So another way to go is to win and consolidate completely in the west and thus the Med/N. Africa as well and that includes beating Britain (see the dreaded sea lion). So maybe some big political POD like a fascist Britain. But of course the USSR will be seeing this and likely making their own POD's.
Another way to go is have the USSR considerably weaker compared to OTL so that the whole rotten edifice does collapse and there is little organised resistance by the time they get to these three cities. So maybe some new Soviet civil war/coup etc?
The big problem here is while the Axis beating the USSR is always going to be a massive stretch, your ATL goal it trying to do it faster.
*that 'when they met them' is the important distinction, because the plan was to find and destroy them. But when they thought they were meeting, finding and destroying the Red armies ability to fight, thanks to their failures they weren't
**In the west Germany invaded France and the Lowlands with 150ish Divs, they invaded the USSR with what 190-200ish including all Axis countries. But not only was France and the Lowlands a considerably smaller area to concentrate forces in and to fight in compared to western Russia. But on top of that the fighting was limited to a much smaller and thus concentrated sub area of that, and the armies they fought were smaller and famously it was over quickly.