There was a significant post-hoc debate about this subject in the United States, which influenced the decision making around the Korean War--I wrote my thesis on that subject so that's how I come by most of this information.

The short version is that we tried. Saying we could've "blocked" the communist takeover ignores the realities of the situation on the ground after WWII. IIRC Truman had a line about using the (defeated) Japanese to hold off the Communists, which ought to give you an idea of how grim the situation was for Chiang Kai Shek and the nationalists. This was a war that had begun before WWII and would continue after.

At the close of WWII we're slow-walking the Japanese out of China to give the Kuomintang (KMT) time to get to the Japanese and accept their surrender so the Communists can't. At the same time, the Soviets are squatting on Manchuria to give the Communists time to get organized behind them before they withdraw.

We're also providing money, guns and troops to the KMT, the last to hold strategic points in the KMT rear so that they can get to grips with the Communists. The Soviets are doing the same for the Communists.

In addition to being hilariously corrupt and hurting its cause as a result, the KMT alienated their own supporters by firing huge numbers of troops for cooperating with the Japanese occupation as part of Gen. G.C. Marshall's attempt to create a unity government.

The mission failed, weakened the nationalists fatally, and led to Truman being blamed for "losing China," which affected U.S. policy when the Korean War broke out.

English books on the Chinese Civil War are hard to find. For my research I relied on OA Westad's Decisive Encounters and The Wars for Asia by S.C.M. Paine.

Edit: shoutout to /u/catfulu to picking up where I left off.

I can’t speak too specifically about China, but the important thing is that containment wasn’t about opposing communism everywhere at any cost. Kennan stressed that the USA had limited capabilities, so must limit itself to areas of vital security interests. For him, this was Central Europe, Britain, and Japan. He, as well as more long lived members of the Truman administration such as Acheson, believed that China was not a vital source of resources for the US at the time, thus did not require a full on engagement. There was also a fairly pervasive (and eventually accurate) belief that China could represent a new example of Titoism ie it would not be a Soviet puppet, nor would the two nations remain allied in the long term. As a consequence it’s fall wasn’t as significant.

Sources

Leffler: A Preponderance of Power

Gaddis: Strategies of Containment

Sorry in advance if this isn’t up to standards, any feedback would be helpful.