The OP's question was how the SU would look without WW2. I assume that means that the war doesn't start, not that the Soviets don't get invaded, which is an interesting question too, but a different one.
Key issue: Why doesn't WW2 happen? If the Nazis don't take over Germany, that's very different from Hitler dies in June 1939, and his successor backs off from war over Poland. Let's minimize the other questions and say Hitler dies of natural causes in June 1939, before too much momentum for war with Poland has gathered. His successor, maybe Goering, pulls back from war.
Is there still a pact between Germany and the Soviets? Not the same one, of course, and any economic pact that was reached would probably be less favorable to the Soviets because the Germans would have other sources of the raw materials, at least until they ran out of hard currency.
Speaking of which, Germany would have to cut back on its rearmament in a major way without the loot from Poland, due to lack of hard currency.
The Soviets would probably stagnate without an immediate external threat to bring them together. Stalin's old cavalry cronies and associated "yes men" would continue to dominate the military, with no sharp military reverses to reveal their incompetence. Stalin would continue the purges at the lower, but by no means trivial level they operated at until World War II historically and resumed after it until Stalin's death. Would there be another Great Purge? Only if Stalin felt threatened, which was remarkably easy to produce, given his personal demons.
Assuming that Stalin lives until 1953, as historically, after his death the Soviets would probably liberalize somewhat, as they did under Khrushchev historically. One impact of no World War II at that point: the western border SSRs (Ukraine and ByeloRus) would have avoided taking the brunt of the World War II fighting, and assuming no more mass starvation episodes, they would emerge from the Stalin era (a) more economically and demographically powerful relative to the rest of the SU, and (b) Less tied to it by fear of attack from the West. Result, any move to liberalize would have to cope with stronger Ukrainian and ByeloRus nationalism.
Without World War II, I'm guessing that eventually Japan bleeds itself out in China, with the Soviets helping that process along. Does the Soviet Union eventually invade Manchuria? Under Stalin, probably not unless/until Japan is near collapse.
And then there is the question of A-bombs. No World War II probably equals no A-bombs until the 1950s. Who gets them first? The US would have the industrial capacity but little incentive in the absence of war. The Germans and Brits would have the scientists, but neither would have a lot of spare money. France? A contender, but probably not the first. The Soviets? A wild card. If Stalin got interested and stayed interested and didn't purge key people, the Soviets could potentially be first with an A-bomb, simply because they put massive resources into it and others stayed at research levels. Equally possible: a covert A-bomb race where several countries got A-bombs, but decided to keep them secret weapons in an effort to keep hostile countries from gaining the key knowledge that they were possible.
I'm skeptical about the ability of the fiercely nationalistic Europe before World War II to manage the transition to nuclear weapons without a war. Nukes would turn them into scorpions in a bottle, with even less warning time than the US and Soviets had during the Cold War. If the Brits or Soviets were first, maybe they could avoid war. Nazi Germany or the Japanese first? I would be very surprised.