Let's put it this way; I'll give an honest answer.
We can rule out any sort of invasion whatsoever after the US manages to get an extremely large stockpile of nuclear weapons. The only real window is in the immediate aftermath of a nuclear war and, well, the Soviets can't conquer enough that they won't possibly lose a few population centers alone to that. (In addition to other bombing).
Note that the British and Americans were already in Persia and India. In order to take out any attacks or bombing runs being launched from those regions, the Soviets would have to invade both there along with into Western Europe and into East Asia. So, we're talking about a front that stretches for thousands and thousands of miles, with a population that has been exhausted by military casualties and is starting to approach the bottom of its manpower barrel.
Let's look at our other assumptions: an invasion of North America. Recall that in the leadup to the Soviets entering the war, the US engaged in operation Hula, the transfer of 149 vessels and the training of 12000 Soviet sailors in preparation fro the Soviets to assist in the invasion of Japan (southern Sakhalin and potentially Hokkaido). The Soviets did not possess the sealift capability, on their own, to go a few hundred miles and put a sizable number of troops in Japan proper. And, by 1949, the Soviets had returned most of those ships that it had been lent. Both the British and Soviets returned equipment to the US they did not wish to purchase. By retaining the vessels, the Soviets would have to come up with some way to pay for it... which isn't going to be possible. they're too deeply in debt and they've nearly shot their load by now. (I'm assuming that Hula didn't have a clause saying the ships were going to be returned. If it did, it makes it that much harder)
So, not only do the Soviets not have the sealift for an operation, they won't be able to build it anytime soon, and any massing of ships will be noticed by the US (where the massing of ships has to take place at, Vladivostok, isn't exactly far from Occupied Japan. The US would easily notice such a buildup... which could easily be stopped.
And, to put things lightly... Alaska isn't exactly important terrain to invade. it's about as far from it as possible. By occupying the land, you are only overstretching yourself while at the same time allowing the US and Canada to trade miles of territories for lives. Until they get to Vancouver, the Allies just have to delay and stall. Bleed the Soviets dry (and they were dry. Nearly 9 million lives lost for the Soviets so far, just in the military, while about 22 million more military casualties...) The Soviets can't afford to throw away a million troops in some harebrained scheme to invade North America.
After all, the Allies just have to hold long enough in the west for the Soviets to start to run dry (Lend Lease was still a significant factor). The Soviets will pillage their puppet states until they are dry, which is not going to be a great way to build support. All the while, the US is churning out an endless number of aircraft and tanks to be used on the battlefield.
The only thing that might save the Soviets the loss of the far east (the US was in a far better position to invade Asia than the Soviets North America) are the Chinese. Of course, it depends on how early the Soviets intervene and if the CCP wins. Oh, and if the Soviets decide to try and talk the Chine into counterinvading into India/Indochina, they lose all the support that might have existed for those regimes.
In the end, the best the Soviets can hope for is a stalemate in the west as their cities are bombed and their invasion fleet into North America is shot up in the water or shelled on the beaches. And, if things don't go quite their way, it is likely they could be pushed all the way into Russia proper, if not further. (The yellow press is not going to sit on atrocities that the Soviets committed while at war. The NYT might have covered up quite a bit of the Holodomr and other similar actions, but that won't stay unnoticed for long.