I don't believe the US was ignorant in this regard. As early as 1962, in a National Intelligence Estimate publication:

Sino-Soviet relations are in a critical phase just short of an acknowledged and definitive split. There is no longer much of a fundamental resolution of differences. In our view, the chances that such a split can be avoided in 1962 are no better than even.

In fact, IMHO, the US took full advantage of the Sino-Soviet split by normalising its relationship with China. As Mao sought rapprochement via Pakistani channels, Henry Kissinger secretly visited Beijing and paved way for Nixon's state visit in 1972.

I actually once wrote a brief paper on this, but about the Eisenhower administration. Nevertheless, it might provide a bit of background to you. Let me lightly edit it and put my sources at the bottom. Because the paper itself is too long, I'll copy and paste some from my précis, which is a tad informal.

Essentially, the tl;dr of it is: the intelligence community (IC) knew about the Sino-Soviet split as early as the 1950's, but politicians, mostly in the State Department (DOS) believed that efforts to try to split the USSR and PRC would actually bring them together. So the answer is really to rephrase your question from "Did the US know about the split?" to "Why didn't the US take advantage of the split?"

---

The U.S. intelligence community gathered information, analyzed and presented reports about Sino-Soviet differences as early as 1959. Several National Intelligence Estimates indicate that the United States intelligence community was giving a sober, realistic assessment of the possibility of Sino-Soviet conflict along ideological, practical and economic lines; however, this was clearly not translated into policy by the Eisenhower Administration. The question becomes: if the United States, or at least, the U.S. intelligence community knew that there were differences between the People’s Republic of China and the Soviet Union, why did this not translate into policy to exploit these differences?

The answers appear to lie in the State Department. Some in the administration, such as Gordon Gray, Eisenhower’s Special Assistant for National Security, advocated taking actions to split China and the Soviet Union; however, State Department officials, specifically Secretary of State John Foster Dulles and Undersecretary (later Secretary) of State Christian Herter did not believe that the United States could do anything more to split China and the Soviet Union. Many believed that efforts to split the Soviet Union from China would actually only serve to bring them together and render them more closely aligned; however, this differed from intelligence assessments and certainly it differed from the Nixon-Kissinger policy in 1971-2. Why did the State Department hold a different view of the potential of policy to expose the differences in China and the Soviet Union than the National Intelligence Estimate, which is prepared by the U.S. Intelligence Board, which is comprised of Central Intelligence, State, and intelligence department from the Navy, Army and Air Force, National Security Agency as well as Atomic Energy Commission? Did the State Department have policy differences or problems that led them to conclude that they could not take action? Was the State Department relying on different information from that supplied by the National Intelligence Estimate or did it disagree with the conclusions therein? Was the State Department still suffering from the purges of suspected communists and thus relying on poor counsel from within the Department?

Many of the answers to these questions can also be found in the basic theoretical assumptions that underlie virtually all American foreign policy. Neither State Department officials nor any other officials had a complete understanding of communism as an ideology, and as such, many held many mistaken or exaggerated views about how an alliance based on communist ideology was different than any other alliance or different from any other alliance based on a different ideology.

To begin, several theoretical premises of United States foreign policy during this period must be articulated. First, communism, in all its forms, was anathema to the interests of the United States. This seems self-evident, but its importance cannot be stressed enough. What is most significant about this first premise is that communism, in all its forms, was to be fought. While this premise could have been refined to articulate criteria of what it is for a nation, party, organization or person to be “communist,” or the term “communism” could have been defined in such a way that it could be boiled down to more easily recognizable components, cogent depictions and effective communication never took place. Thus, the Soviet Union was “communist” and the People’s Republic of China was “communist,” as were Yugoslavia, Cuba, Korea, and Vietnam, notwithstanding significant ideological differences in precisely what “communism” meant to ruling elites in each nation. Most importantly, the practice of Communism was uniform and without distinctions; there were no sub-categories of communism: the Soviet Union’s communism was the PRC’s communism was Cuba’s communism. It should be noted that the United States and other Western Powers did not draw this conclusion immediately, but by 1948, it was certainly accepted by President Truman and other mainstream Democrats and Republicans.

Secondly, a premise of United States foreign policy was that inaction or isolation was no longer a permissible foreign policy option for any American politician, Republican or Democrat. Although Democrats and Republicans differed with one another and within their own parties about how much of a strategic commitment the United States should make in different parts of the world and to which parts of the world that commitment should be, they both believed that the United States needed to actively contain the global spread of communism. Thus, a gain for communism abroad, regardless of the circumstances, was a loss for the United States. Accordingly, Truman “lost” China, Communists “took” Cuba [from us], Roosevelt “gave away” Eastern Europe to the Communists, etc. Implicit in statements such as these is the assumption that those nations or territories that “lost” to Communism were somehow possessed by the United States. This sense of global possession and a responsibility of global protectionism were byproducts of this second premise: inaction and isolationism were dead.

Thirdly, communism as an ideology was different from other ideologies in that it cemented alliances more thoroughly than alliances bound by other ideologies. This logically stemmed from the first assumption that communism in all its forms must be opposed. It perhaps seemed logical and intuitively correct, following balancing theory, that whatever forces in communism forced the United States to oppose it without nuance would also force those communist forces to ally without nuance. Whereas capitalists alliances, or alliances based on non-communist ideologies could fall pray to divisive factors long recognizes as universal by foreign policy scholars, differences in areas such as in national interest, personality disputes between leaders, border disputes were thought to exert less of an effect on communist alliances. National Intelligence Estimates, scholarly writings, and basic political assumptions by politicians reflected this belief. Many of the Eisenhower’s Administration officials believed that efforts to split the Chinese-Soviet alliance were operating on a traditional balancing theory, when they stated that opposition or attempts to exploit the Split would give the Soviets and Chinese additional impetus to stay together in light of the common threat.

From these assumptions, we can begin to understand the obstacles that deterred recognition of the Sino-Soviet Split by Eisenhower Administration officials. Accepting the third premise, for instance, it seems a poor use of resources to attempt to create or act on a split of an alliance that is stronger than conventional alliances. Accepting the first premise, that all communism must be opposed, leads one to draw the conclusion that communist regimes, following balancing, would all ally to oppose the United States. Accepting the second premise changes the way foreign policy debates are framed in the United States. Whereas in Wilson’s day, the United States Senate rejected the League of Nations, and the United States fell back into isolationism in the Inter-War period, politicians no longer debated on the merits of isolationism but instead attacked one another on matters of tactics and strategies in fighting communism.