How difficult of a problem was this?
It's called the Cold War. Both sides tried out out-develop and out-manufacture each other, in an arms race, with neither gaining the superiority needed to ensure a victory until they mass-deployed nuclear missiles, which created MAD (Mutually Assured Destruction). The Cold War is proof that neither side had a military path to victory against the other.
So when someone says, "Side X could have defeated Side Y," take a look at the weapons systems developed for the Cold War with idea that these weapons were prerequisites to any successful traditional assault on the other side of the world. The catchword here is "intercontinental."
For example, the B-52, an intercontinental bomber, was bid in 1946 and began service in 1952. Criteria for its development must have begun soon after VE day, if not while the war raged. They military knew exactly what it needed to defeat the USSR, and it didn't have those tools. Importantly, it wanted an bomber with a 5,000 mile range, which is double the range of the B-29.
The Cold War wasn't just war by proxy, it was an era where each side fully expected to fight the other to the death, and each side was actively preparing to do so. Forty years later, at the fall of the Berlin wall, neither side had declared victory.
Who would win if the Allies and the Soviet Union fought? Nobody. Despite the greatest economy in the world, stalemate was the best that anybody could produce.