There was no willingness about it. The Red Army had something like 11 million men under arms in 1945. Meanwhile, America was already in the process of beginning demobilization later that year. While America had more men overall, they also had significantly more naval forces. If it came to a ground war, they'd need the British Army and newly rebuilt French Army to achieve operational parity.

Sure, America had nukes, but short of a willingness to drop dozens of them on the very same occupied people they would supposedly be going to war to liberate, and ignoring for a moment that America only had a handful in 1945, the only way to beat the Red Army was to squander the lives of millions of Allied soldiers.

That's ignoring the fact that Europe was staring down the barrel of a truly devastating famine if farmers were unable to get to work in early 1946. The Dutch had endured famine in 1944 and the Soviets would suffer through a long one (1946-1947) already. What would another year of devastation and death do to the continent?

As it was, Germany already faced food shortages in 1945-1946, though you can probably make the case that those were caused by American policy on the matter (Roosevelt wanted a much more devastating peace than Truman). There would be periodic shortages elsewhere. And if these shortages were ongoing when the specter of a flu pandemic cropped up in 1947, especially with governments unable or unwilling to quarantine war-related operations, then things could have gotten very nasty indeed.

There was no willingness about it.

I have to take issue with /u/Imperial_Affectation 's assertion, as I don't think you can answer this question without addressing what happened at the Yalta Conference of February of 1945. There, Churchill and FDR conceded that Stalin could have his "sphere of influence" in Europe after the war. What they wanted from Stalin, as well as how freely they expected the Soviet sphere of influence to evolve after the war, also explain why they agreed that the Soviet Union should build this sphere.

There is no doubt that the fact that the Red Army occupied much of the area that Stalin wanted for his sphere of influence played a large role in Stalin's influence over the Yalta Conference. At the same time, however, this cannot explain why the United States changed military plans in order to allow the Red Army the right to liberate Prague in order to bring Czechoslovakia into the Soviet sphere. FDR acquiesced to this demand because he wanted two things from Stalin: a guarantee that the Soviet Union would remain a part of the United Nations (which the "Allies" called themselves at the time) after the war, and a commitment to enter the war against Japan after the defeat of Germany (keep in mind that the atom bomb had not been proven at this point). In exchange for for these promises, FDR gave Stalin something that seemed reasonable anyway: the opportunity to organize an alliance of nations friendly to the Soviet Union to act as a buffer between the Soviets and the Germans, who had invaded Eastern Europe twice in the last thirty years. This sphere of influence, Stalin agreed, would have free elections after the war. In other words, Stalin would organize their postwar provisional governments, but the citizens of these countries would have the final say on how they were to be governed. One can very easily look back and see that Stalin would renege on this stipulation, but FDR did not know that at the time (for which he was strongly criticized in the coming years). The fact that the Red Army already occupied are loomed over most of the region that Stalin desired to influence after the war made FDR's decision to agree to a "sphere of influence" in exchange for short-term and long-term Soviet-American cooperation that much easier to make.

The foundation of the Soviet empire was laid at Yalta, Very briefly, Stalin worried after FDR's death that Truman might not honor the Yalta Agreements, and so he diverted forces aimed at Berlin to liberate Prague before the American army could arrive there. Stalin's fears proved unfounded, however, as the Americans halted their march even under Truman's leadership. Stalin liberated all of the nation's that he hoped to liberate, and every nation liberated by the Red Army subsequently became a part of the Soviet empire.

If you are asking why after the war, with the rise of the Cold War, that the United States favored containment over the rollback of Communism in Eastern Europe, then I'll be happy to address that question as well.