Actual Operation Unthinkable would have been a military disaster for the west. The Western formations could compete man to man and tank to tank, but there were half as many tanks and 1/4 as many men. They would have air superiority, no question, but this is still a time when that can't guarantee total success and the Soviets will be able to dispute air control in key areas during their offensives.
Theoretically, if we lived in an alternate universe where public opinion means nothing, soldiers are happy to stay in uniform for indefinite periods of time, and everyone agreed that the USSR needed to be destroyed at any cost, they could have defeated the Soviets. The total population and industry figures for the west and western occupied areas gives them theoretical superiority, at least long term. USA+Canada+Mexico+Brazil+Commonwealth+Japan+Italy+France+Low Countries+Norway+Greece+West Germany. However, this would require total dedication from the United States, Canada and Western Europe, they would have needed to raise more divisions than they had, they would have needed to reactivate all the soldiers who got sent home after the fall of Germany and Japan, and keep cranking out tanks, airplanes and other war materials as if it were still war time over the 1945-1946 period.
Conflict in January 46 = not going to work for the west. If the west kept up production and raised new formations without skipping a beat when the Nazis got dealt with, they might have been ready in time for summer 46 or summer 47. They will need to forget about trying Nazis for war crimes and instead start shipping the German military survivors back into uniform and recruiting from the population there. They're already very worn down but they could still plausibly raise a number of formations.
Strategic air campaign smashing industry in the USSR from Northern India or Persia or somewhere like that will probably be a requirement for a successful operation. Thus, Indian independence will need to be delayed. Since this is a magical fairy land where public opinion means nothing and everyone wants to take down the Soviets, that's ok. Atom bombs will inevitably need to be deployed, probably directly onto Moscow. Actually hitting Moscow might be possible if this is taking place at the time when the Soviet's high altitude air defenses are not very good, but this window will close eventually, and by '49 the USSR will have their own a-bombs. So the war would need to be over by then or it could get ugly.