Thanks for any/all answers in advance!
Short answer: Yes, they did AND it's complicated.
It's perfectly feasible to argue that the human, economic, environmental, and infrastructural devastation visited upon the USSR (and Eastern/Central Europe more generally) probably had a greater impact on the thinking of decision-making figures in the USSR than in the 'Western' allied nations. It's also crucial to note that what we end up calling 'the Cold War' was fundamentally an ideological conflict rooted in two differing visions of modernity – both sides believed that their vision was right and universally applicable, both sides believed in their own concept of ‘freedom.’
The emergence of the Cold War was not predetermined, and it was not inevitable. It came about as a collective result of ideological clashes, unilateral decisions, political disagreements, and misperceptions. In the aftermath of World War Two, the Cold War emerged as the former allies clashed over a wide variety of issues such as the status of their defeated enemies, Soviet actions in Eastern Europe, US policies towards Western and Southern Europe, and even the resumption of the Chinese Civil War between the Nationalists and the Communists (which even further complicated matters).
And it is crucial to emphasise that no one side was to blame for the Cold War’s emergence. It had long, medium, and short-term roots. It may seem at first glance that Stalin was behind many of the events that led to the Cold War. But in reality, the question of blame is utterly pointless. There were misperceptions and misinterpretations on both sides. The Americans thought the Soviets were behaving far more aggressively than they actually were, a sense reinforced by analyses of the Soviet mind set coming from leading US diplomats in Moscow. They also confused communist-aligned groups fighting in civil wars with Soviet backed forces attempting to make inroads into southern and western Europe.
Despite perceptions that Stalin was looking to expand Soviet influence, his real interests lay in solidifying control over eastern Europe and resolving the questions of Germany’s post-war status. The collapse of wartime trust created a tit for tat retaliatory system that dominated relations between the United States, Britain, and the USSR into 1946. Just as important was (and here we circle back to your opening question) the impact of WW2 on the USSR. Stalin (and other key figures, if we're being honest, but let's consider the guy at the top) was determined not to let the devastation that had been visited upon the USSR ever happen again. He also perceived that there was a 'Western encirclement' of the USSR taking place. While the reality might have been different to Stalin's perception, the situation in 1945 makes his belief on this explicable. Just look at this map:
[This and other other maps can be found here]
If you're a paranoid leader sitting in the ruins of a state that has been invaded and devastated twice in the last 45 years, it's not beyond the realms of possibility that this could happen again. And Stalin being aware of the post-1945 extent of US military and economic power helps to explain this.
While the 1945/1946 Iran crisis (which is a topic in and of itself) was evolving, a senior American diplomat in Moscow was asked for his thoughts on what the Soviet leadership was all about. George Kennan was a well-educated Sovietologist and career diplomat. His ‘long telegram’ of February 1946 was so-called because – at 8000 words – it was the longest telegram in the State Department’s history up to that point. He painted a picture of the Kremlin as aggressive and grasping, scarred by war, but eager to exert wider control in the world. His words had a galvanizing effect on the Truman administration, helping to solidify a growing sense that the USSR was definitely up to no good. It is crucial to note, though, that Kennan did not advocate for a global, comprehensive form of containment, His thinking was focused on a calculated policy of denying the USSR access to crucial German and Japanese resources, while using those resources to aid in the rebuilding of a devastated world. Influenced by diplomats and thinkers such as Kennan, the Truman administration moved along a path which led to what was termed containment. Rather than reaching an accommodation with the USSR in the post war period, a policy of containing the seeming global spread of communism emerged as a key part of America’s approach to the world. Everything that the Soviets did started to be seen through the lens of aggression and expansion. Even concessions were seen as somehow suspicious. Events around the world – and not just Iran – helped to harden this sense of threat and move the Truman administration towards the strategy of containment.
By 1950, the Cold War was well and truly on. All parties involved had contributed to its emergence and solidification. While Stalin was indeed a key player, there is no way you can discount the influence of Harry Truman, Winston Churchill, and many others in the emerging standoff. It happened because of several factors, including (but not limited to):
The above is - of course - a relatively cursory exploration of the issues. There's a lot more to be said about the 1945-1950 period, including the Turkish Crisis, the status of Poland, the 'German Question', the Marshall Plan, the Baruch Plan, the Berlin Blockade, and much, much more. Always happy to follow up with additional detail if required.
Kind regards,
Malcolm
And here are some suggestions for reading (and some of the sources I've used to compile this answer, which is actually paraphrased from an undergraduate lecture I do each year):
Costigliola, Frank, Roosevelt's Lost Alliances: How Personal Politics Helped Start the Cold War (Princeton: Princeton University Press, 2012)
Craig, Campbell, and Sergey Radchenko, The Atomic Bomb and the Origins of the Cold War (New Haven, CT: Yale University Press, 2008)
Engerman, David, 'Ideology and the origins of the Cold War, 1917-1962', in Leffler, Melvyn and Odd Arne Westad (eds.), The Cambridge History of the Cold War, Vol.1 (Cambridge: Cambridge University Press, 2010)
Kennedy-Pipe, Caroline, Russia and the World 1917-1991 (London: Bloomsbury, 1998)
Mastny, Vojtech, The Cold War and Soviet Insecurity: The Stalin Years (New York/Oxford: Oxford University Press, 1996)
Westad, Odd Arne, The Cold War: A world history (London: Peguin, 2018)
Zubok, Vladislav, A Failed Empire. The Soviet Union in the Cold War from Stalin to Gorbachev (Chapel Hill: University of North Carolina Press, 2007)