There was a lot of denial about when the Soviets might get the bomb. The estimates made in 1945 was that it would take 5 years. In 1946, people then said it would take 5 years. In 1947, another 5 years. 1948, 5 years. 1949, they got the bomb... 5 years early! Surprise and shock!

(4 years was still sooner than most people thought, but it depends on when you wanted to say they "started," and in any case, these estimates were not grounded in any real intelligence. At best they were grounded in pre-war understandings of the Soviet uranium mining potential, and at worst they were grounded in lousy stereotypes about backwards Russians.)

But in terms of whether anyone seriously floated the idea that prior to the Soviets going nuclear, the US/NATO ought to preemptively attack them... not really. Partially this was because people were in denial about when the Soviets would get the bomb, or even they were even trying to get it. Partially because they were for about half of that time genuinely pursuing the possibility of international control of nuclear weapons and trying to stem off an arms race. And, perhaps mainly, it was because all of these countries had just fought a really unpleasant war, and the priority was rebuilding Europe and Asia, and consolidating those places against Soviet influence and incursion. Which is to say, pretty much nobody thought that it would be politically acceptable for the US/NATO to turn around and start a new, protracted war with the Soviet Union out of nothing.

A war with the Soviets at that point would not have been easy. Aside from the fact that the US and Europe were largely demobilized (and in the US, trying to cut back military forces even further than the generals and admirals wanted, to save money), and trying to restart their peacetime economies, and all that, the fact remained that 1) the Soviets still had a very large and by this point well-seasoned Army that had just fought off the Nazis and consolidated a huge amount of territory, and 2) the atomic bomb stockpile was pretty small for much of this period and the delivery methods (B-29s) were pretty limited. During the time of the US monopoly the US did not have the capability to end the war with nuclear weapons alone. They'd be getting into a protracted conventional war that might occasionally have nuclear weapons used but the odds that the atomic bomb would make it a definitive win for the US (and that the Soviets would not be able to manage to take most of Western Europe in the process) would be low.

And the US would not even be able to strike most Soviet targets without using extensive foreign bases, anyway, some of which could be compromised by a Soviet counter-attack. As of 1947 pretty much zero atomic bombs were assembled and ready to go (they had material for them), and it took several years to get the bomb production system up and running after the lapsed period since the end of World War II. These were all essentially WWII-style atomic bombs, with almost no improvements implemented in the stockpile until around 1950 anyway. The US did not even formalize the policy by which the President would order a nuclear strike until 1948. Which is just to say — this was not some sort of well-oiled, well-organized ship for most of this time, but a rather haphazard thing that only started to really become what we think of as the Cold War nuclear complex by the very end of this period, and most of what we associate with the Cold War deployments and capabilities didn't start until the 1950s.

All of which is to say, it would have taken a lot of political capital and political will to imagine beginning something like that from nothing, and nobody had that or was really looking for that. It would have been an ugly, expensive, unpopular gamble. Best case scenario is that now you've got to worry about rebuilding Russia on top of everything else, and whatever that would look like in the long term. Worst case scenario, the Soviets take Western Europe and who knows what else, and you've made the Cold War even nastier than it needed to be. None of this was in the slightest attractive, especially when no one knew if the Soviets were actually making a bomb and when they might get it. Denial was much easier on every level, a trend we have seen in many other places before and since. (The Soviets had their own denial about the atomic bomb, too — basically it went almost totally undiscussed in public forums until after Stalin's death.)

A good book about the time of the American nuclear monopoly is Michael Gordin's Red Cloud at Dawn, which is basically looking at the Soviet nuclear program but also looking at how the Americans and Europeans were thinking about its possibility in this time.

Adding to Alex's great response, it's important to remember how much happened in those early years of the CW, between the end of WW2 and the first Soviet atomic test (and the roughly contemporaneous victory of the communist forces in the Chinese Civil War). It's kind of a mugs game to try and pin down when the Cold War started (you can trace the roots back to 1917 or earlier - Arne Westad starts his survey of the CW in the 1890s). The formal creation of NATO in April 1949 is only a few months in advance of the Soviet test. In Timothy Sayle's recent book Enduring Alliance: A History of NATO and the Postwar Global Order (which is very good, by the way), he argues that - certainly in the early days - NATO's primary mission, was not military containment of the USSR (i.e.: preventing an invasion into Western Europe), but to resist Soviet political blackmail over issues such as Germany. Moreover, Sayle contends that NATO (at this early stage) was as much a tool to reassure domestic audiences in Europe as it was a means of resisting perceived Soviet adventurism. Finally, it also existed to provide a framework through which a rebuilt West Germany could be safely further integrated into Western politico-military structures without causing undue alarm amongst those populations who had so recently experienced the events of 1939-45. From my POV, I find much of what Sayle argues persuasive and useful when it comes to thinking about NATO's Cold War role.

Cheers,

Malcolm