The Germans ravaged eastern Europe and parts of Russia, but a lot of the territorial gains the Germans made were in areas already devastated by Russians. Stalin ordered that anything which may be of use to the enemy be burned or destroyed regardless of its necessity to civilian populations.

Starting with the first Five Year Plan in 1928 Stalin had ordered that new heavy industry should be developed east of the Urals. Shortly after the invasion began Stalin ordered the start of an economic mobility program that saw industry west of the Urals broken down step by step, shipped east of the Urals on train, and then reassembled. For the most part, the Russian industrial plant survived the war unscathed. Industrial output dropped during the war due to shortages of raw materials.

The post-war recovery was driven by two things: reparations from Germany and nations who aligned with Germany and, since they controlled it, the Russians stripped what they needed to rebuild their economy from eastern Europe. For the next several years the focus was on industrial output rather than consumer goods and agriculture. There was an attempt made to take out a loan from the US, since the US was the only major nation to come out of the war with excess investment capital, but ideological differences between communism and capitalism made this impossible. So the result it that the Russian laborer bore the burden to rebuild the economy while living in a similar state of austerity to that experienced during the war.

As the saying goes, the Russian peasant has a strong back.

A goodly portion of the answer is found inside the question itself: in spite of losing a vast amount of people and resources, Soviet armies had managed not only to eliminate Hitler, but establish Soviet power in half of the European continent. This fed the perception that the USSR was a major and emerging power much like the United States.

The key to this recovery and power projection through armed force was the Soviets' planned economy. As /u/International_KB has written extensively and far better than I could have on this, the Soviets management of the wartime economy was both extreme in its effectiveness and ruthlessness. Although Soviet weapons might have been relatively crude compared to their contemporaries, their wartime production strategy that produced them was both highly sophisticated and logical. Soviet production lines emphasized planned obsolescence, simplification of design, and a Taylorist streamlining and efficiency. The gravity of the fascist threat justified the relative indifference of the state to the impact this mobilization had upon the larger civilian population. This allowed the Soviets to field a truly massive and modern army.

Since power is often very much about perceptions, it is instructive here to contrast two novels, Arthur Koestler's 1940 Darkness at Noon and George Orwell's 1948 novel 1984. In Koestler's novel, a former Communist functionary Rubishov is sent to prison and after philosophical discussion and torture, confesses his treason to the state. Although the country is not referred to by name and the dictator is referred to as Number One, a number of clues in the narrative clearly point to the Soviet Union and Stalin. In contrast, the three main Socialist blocs in Orwell's distopia are massive polities stretching over several continents. The state is omnipresent, but impersonal to the point of an abstract dehumanization. Oceania's dictator Big Brother exists as an embodiment of the party's total hegemony devolving into yet another lever the system uses to mobilize its population. As 1984's protagonist Winston Smith thinks about his life, he is increasingly unsure if Big Brother even existed as an actual human being and his exploits have been transmuted into legend. In contrast, Koestler's Number One is a deeply personal figure whose mercurial decisions provide the justification for him to cull out any perceived political rival. For example, Number One's shifting rationale for submarine design provides a rationale to liquidate an admiral who refused to tow Number One's line that smaller coastal submarines were the ideal expression of Communist naval power. As Rubishov's interrogator explains to him, the admiral's intransigence on this point gave Number One no excuse but to eliminate him via a show trial and execution. In Koestler's 1940 novel, the system enables its own abuses whereas Orwell described a system that had become a dehumanized power onto itself, or as one of Oceania's partisans puts it, the future is "a boot stamping on a human face - forever." Although the differences between the two novels could be chalked up to aesthetic decisions of the two authors, it is telling that Orwell conceived of his depersonalized distopia in 1944 as it was clear that three large planned economies were carving up the world into spheres of influence.

The reality was that Soviet power as a whole was relatively ephemeral after 1945. Both war and reconstruction reflected the strengths of the planned economy, but it could not adapt easily to the rigor of peacetime consumerism. The Soviets were still wedded to Taylorist production models well after the West had moved on to more advanced forms of organization and management. The planned economy could produce a modicum of consumer comfort and occasional luxuries, but its drive for massive economies of scale paradoxically translated into chronic inefficiencies and shortages in the civilian economy. Although Soviet military power remained competitive with the West, it fell behind in other key indices. Behind its sophisticated military hardware and showcase technology like Sputnik was an economic system that was its own worst enemy.