I'm interested in the period between the war ending and the Soviets making their own bomb. Did they have a plan? Were they expecting a first strike?
The Soviets were always extremely paranoid, in no small part because they expected NATO (and specifically the USA) to have the same aggressive attitude towards them as they had towards NATO.
In other words, the Soviets fully expected the USA and its allies to launch a first strike on the USSR at the earliest opportunity when the USA considered it a fight they could win.
The USSR at the time directly after WW2 did not have nuclear weapons, they only detonated their first one in 1949 (and only managed that because they had the Manhattan project well and truly infiltrated almost from the very beginning). But, knowing the work of the Manhattan project, they will also have had a decent understanding of the size and limitations of the US nuclear arsenal at the time, knowing full well how small the US stockpile of nuclear weapons was, and how limited its ability to employ those weapons against the USSR. Basically, until the B-36 arrived in numbers the only aircraft capable of launching a nuclear strike against the USSR was the B-29, and that one just didn't have the range to hit any militarilly or politically significant target in the USSR (except maybe some Pacific coast ports and airfields if used from Japan), and would be at severe risk of being intercepted by the Soviet air force trying to penetrate Soviet air space on the way to their targets.
Also, the USSR had significant stockpiles of chemical weapons, and almost certainly stockpiles of biological weapons as well (especially plague and anthrax, but possibly also tularemia and smallpox).
They also had a serious numerical advantage, especially in the European theater, and far shorter supply lines into Europe than does the USA. There was no significant Soviet submarine fleet as yet right after WW2 so them blocking the Atlantic supply route between the USA and Europe was not yet a serious consideration (that only started in the 1960s with the advent of large numbers of nuclear powered submarines, many of them armed with nuclear torpedoes and/or missiles, by which time the USSR could have easily destroyed most sea ports on the US east coat and European costs within hours of hostilities commencing).
As to having plans, their plans were likely the same as what they'd done against Germany. Massive combined arms operations flooding Europe with Soviet troops, killing everything in their path that offered the slightest chance of offering resistance. Basically the same thing the Chinese did some years later during the Korean war, ignoring casualty numbers because they knew they could sustain those casualties far longer then could their opponents.
NATO war plans assumed such a mass assault to be the way the Soviets would go about launching a war in Europe well into the 1980s. Which is why NATO placed such significance on the battlefield use of nuclear weapons to take out logistics hubs, highway and railway chokepoints, and troop concentrations. It was basically the only way NATO could hope to contain a Soviet assault long enough for US reinforcements to arrive in numbers. Which in itself caused the Soviets to build their war plans along a massive use of chemical and nuclear (and potentially biological) weapons to destroy airfields and ports in Europe that would receive those US reinforcements, as well as NATO bases potentially containing stockpiles of nuclear weapons in the first minutes to hours of any conflict, before those weapons could be used against the Soviet advance.
Basically then, nothing really changed in the Mexican standoff between the USSR and USA in central Europe between 1945 and 1990, except by the end both sides had large stockpiles of nuclear weapons, both targeted mainly at the other side's stockpiles, whereas in the beginning the only few nuclear weapons in theater would be on US operated air bases in the UK, awaiting the arrival of B-29s to carry them towards and hopefully into the USSR (a B-29 could potentially hit cities like Leningrad and Kiev from bases in the UK though it'd be a one way trip, if they could make it through Soviet air defenses at all).
First, there was no real notion of a
first strikeas it is known today. That's tied to ICBMs and the declared intention of both the US and USSR at the time (and Russia now) to allow an attacker to get a strike in before retaliation, in the very real interest of avoiding launching a counterstrike based on a mistake in the surveillance radars. This would not have been the cases 45-49, the Soviets would have had plenty of time to see bombers coming and react and the number of nukes was limited. So, you're talking more about a very large scale war with a nuclear dimension, rather than how things looked from the mid-60s on.
I believe that the situation was not dissimilar to what is the case in the North Korea standoff, where the people living in Seoul are essentially hostages to dissuade attacks by conventionally very superior forces.
However, besides the hostages, essentially all of Western Europe, the outcome was nowhere as clearcut as one would think. The USSR had massive conventional armies, massed near the borders of East Germany and Poland. The US Army had aggressively demobilized after WW2, as can be evidenced by their early struggle in the Korean conflict in 1950. So the US ruled the air somewhat, and the sea very much, but the USSR had the better ground forces which incidentally provided a very deep buffer between Western forces and the Soviet core resources.
Nuclear arms were limited at the time, with far from assured delivery, especially over distances needed to strike the Soviet heartland. This would not have been a replay of dropping the Nagasaki and Hiroshima bombs over a country that had long been defenseless against air raids and didn't expect nukes. It would have been a long slugging match with occasional Dresden/Hiroshima level strikes at Soviet centers. Modern H bombs are really a whole other level over the A bombs existing then.
Had a war started, the USSR would have had a good chance of running over Western Europe and gaining a full ocean's worth of buffer zone between them and the US. The use of A bombs at the tactical level probably would not have stopped it and the temptation would in any case have been to use them at the strategic level, against Russia proper. Besides the unsinkable aircraft carrier England represents that would have pretty much cut off US nuclear risks. At that point, even if they had suffered grievous losses, the USSR could have presented the US with a fait accompli and either prosecuted the war or agreed to stand down.
It's interesting to note that, whatever the Soviet disadvantages until they exploded their own bomb, Stalin didn't shy away from confrontation, as in the 1948 Berlin blockade. Plus, the Soviet inferiority in bombs and delivery systems didn't really subside until much later, as evidenced by the pressure Kennedy felt safe to apply during the Cuban missile crisis and they essentially continued this strategy for a long time.
So both sides had their strengths and weaknesses, but the USSR would have been able to apply extreme pain against the US's allies in Western Europe using conventional forces. And occupying all of Western Europe may very have been a war-winning endgame. Once enough bombs were around to ensure Mutually Assured Destruction and once the risks of nuclear winter became clear, the whole notion of fighting a large scale direct war became unacceptable, but that didn't happen for a while.