There is a thread with an almost identical question from a year ago, which you can find here.
The cliff notes version of the post there:
1. The US did not believe there were imminent soviet plans to attack
2. The deployment of atomic bombs against the USSR was not completely trivial as it would be in the age of ICBMs
3. The USSR was bloodied, depleted and not eager for another conflict immediately
I would like to elaborate on points 2 and 3 myself.
Early atomic bombs were large and required B-29s to carry a single physics package. The range was not infinite and they could be intercepted theoretically (although I'm not entirely clear on whether or not the Soviets had aircraft or guns that could hit a maximum altitude B-29 in 1945, or whether a B-29 carrying a MK II/III bomb could reach anything close to that maximum). You would in general want to have air superiority before committing to drop such expensive single bombs, but even so, given the slow rate of production, conventional air power would be doing more damage per month on average than the early post-war atom bomb programs would assuming the same kind of mass air raids that occurred in 1944/1945. They would be a useful addition, but not necessarily war winning on their own. As to whether or not this played on the Soviet planner's psyches, that is unclear.
I don't have sources on hand, and I apologize, but the Red Army's demobilization between 1945 to 1948 was quite dramatic, reducing strength from ~10-11 million total personnel to ~3 million, and the demobilization order was given in mid-late 1945 to control this reduction. This would indicate that they did not expect an imminent conflict, either offensively or defensively, but this was also quite necessary considering the state of the USSR. Huge amounts of the country were still damaged, and men were needed elsewhere to help reconstruct and to man the farms and fields. In 1946 there would be a significant famine in the USSR, even with all of that manpower to help.
In the immediate postwar period there wasn't really a plan for immediate war with the West by Stalin and his senior elite.
In particular Molotov and Stalin (2 of the 3 key players in Foreign Policy, the other being Litvinov, though he was somewhat out of favour at this time), thought that war would occur, or at least favourable conditions for war, due to a fall-out between the UK and USA over the post war settlement. There were some signs that this was more than a fall back on Lenin's doctrine as set out in 'Imperialism: the highest State of Capitalism', over 1946 and 1947. These included the different visions of de-colonialisation that these two states shared, with the US favouring a much more rapid withdrawal than the British, and the 1946 economic crisis partially caused by the US forcing the UK to make the pound freely convertible to the dollar, causing a bad slump for British exports for the remainder of the decade. However rather than causing long term antagonism, the (later) effects of the Marshall Plan mitigated much of the economic damage from this early strong-arming by the US, and the British economic weakness led to much closer ties between the US and the UK to maintain the Western Allies commitment to the occupation of Germany. By 1947 the Soviet worldview was in need of significant revision.
On a more practical note there was also a need for a pause in fighting as the Western USSR was in ruins, the economic base greatly weakened, and tens of millions dead. Even with the postwar draw-down in forces the famine caused by the weakness of the Soviet Economy still led to several hundred thousand deaths in 1946-47.
This is not to say that the Kremlin was not expansionist at this time, Stalin felt the War had vindicated his rule and say the future of the USSR as the dominant world power, ready to expand where possible (like in Iran immediately after the war), but direct confrontation was out of the question ( Stalin's economic planners thought it would take 3 5-year plans to put them in a 'safe' position for direct competition with the US, so somewhere in the mid to late 1950s).
(Tony Judt, 'Postwar', William Hitchcock 'The Struggle for Europe' and Vladislav Zubok and Constantine Pleshakov 'Inside the Kremlin's Cold War', Alec Nove, An Economic History of the Soviet Union)
On the subject of Stalin and his views of nuclear weapons, I recommend Craig & Radchenko's 'The Atomic Bomb and the Origins of the Cold War, and David Holloway's 'Stalin and the Bomb' as the best place to start. I haven't read them in several years so I'd not feel comfortable summing them up here.