From Syria and Iraq, it is less then 1.0-1.5k km to Baku, depending on where your air base is, exactly, so doable for both strategic bombers and P-38, Mustang probably was a bit short, but then it depends on whom got upper hand in occupied Iran, maybe allies would have even closer bases.
It isn`t as huge of a problem, if war is already going on, and there are troops and supplies on the way to Europe. In cold war, yes, Soviet surprise attack was a huge factor, because it would take a week or more for any shipping from US to even make it into port in Europe. But in 1945, plenty of ships are on the way, and army is already there.
I don`t see any reason to believe that war will be done in a months. US and UK were far better motorized, which makes large scale soviet encirclement unlikely. Soviets would have to push far greater distance than historically Germans have in fall Gelb, under heavily contested air, and also into rough terrain in Italy, against already highly mobilized and battle ready troops. If they would be done in a year, I would be surprised.
Soviets refuse to cave, so what? You occupy up to Polish-Soviet border, then, if needed, continue small scale advances, while mobilizing your European allies army, and using UK, France and Germany for support and initial repairs, replenishment and so on.
In the end, Soviet army just collapses, from lack of bodies, and food, munitions, fuel ex. In the end, you don`t have to occupy deep, you can get plenty of local support in occupied areas. Once you manage to create local goverments in Poland, Ukraine, Baltic states, ex, US and western allies only need to run relatively small force.
Also, Russians refusing to cave, is just a stereotype. They were smart to not cave when they had more resources and would win long term, but also accepted defeat in case they had to advantage in long term.