No. The Sino-Soviet split was motivated by fundamental differences in national interests, so there is little that a third party like the US could have done to influence it. Furthermore, US policy makers were wilfully ignorant of early signs of the split, which means that they did not exploit the situation until it had become abundantly clear, by the aforementioned opening of Sino-US relations by Kissenger and Nixon.
Differences in national interests
The Soviets and CCP were arguably playing off each other from the start, both looking out for their own interests. There are numerous examples:
- The USSR's piecemeal and misguided assistance to the CCP during its early days, in its conflict with the KMT and Japan, such as the disastrous Nanchang Uprising, support for the KMT which was even greater than to the CCP, the repeated attempts at gaining influence in Chinese territories such as Xinjiang, Mongolia and Manchuria. All this demonstrated that the Soviets were more interested in securing Siberia and gaining satellite regimes than assisting other Communist movements.
- The spectacular failure of applying traditional Leninist revolutionary theory in China (i.e. revolution by workers, rather than peasants) motivated Mao into rejecting Soviet leadership in world communism and taking China on its own, direct path to communism, via the Great Leap Forward. But this simply boils down to a difference in national interests: China/Mao wanted to be independent whereas USSR wanted to retain influence and leadership over all communist states, and this disagreement manifested in areas such as nuclear weapons, which China wanted but USSR under Khruschev opposed.
Wilful US ignorance of split
A minority of the US's Intelligence Community were well aware of the coming split before it became obvious around 1960 and undeniable in 1969. It was widely believed for a long time that the communist bloc stood in solidarity against the West and that shared ideology could trump differences in national interests, and this conviction was hard to shake even in the face of overwhelming evidence. It certainly didn't help that this split developed so soon after the Red Scare; CIA analysts believing in the coming split were considered "heretics".
In fact the only major action that the US took to undermine Sino-Soviet relations was its hardline reaction to the U2 spy plane incident which made Khrushev look weak to hardliners, including Mao, and convinced the latter to move away from the USSR. But given that the incident was counterproductive to American interests, it's highly unlikely that this was done deliberately, and the split was well under way at this point.