Well this is a debate amongst historians on the topic: was Castro "pushed" into the arms of the Soviets by the U.S, or, were Castro's intentions all along to break ties with the U.S diplomatically and economically?

To first answer this question, we must decide what we believe Castro's political persuasion was. First, why would Castro claim not to be a communist? The answer to this is one of two things: either A) He genuinely wasn't a communist in 1959 when he stated as such to Herbert Matthews in a series of interviews, or B) He was a communist, however, seeing U.S intervention throughout Latin America and knowing the longer imperial history between the U.S and Cuba, he lied in order to avoid direct U.S intervention in his revolution.

Whilst Castro himself has stated in his autobiography that indeed he was always a Marxist, having seen the blight of sugar farmers on his fathers estate, and his statements to American media outlets were intentionally deceptive. However, how do we take such a statement? If Castro was so willing to lie for the sake of optics once, who is to say he isn't lying in his autobiography regarding the origin of his Marxist beliefs? Thus, its hard to ascertain whether Castro was truly a communist or not in 1959 when he took power. However I would argue that Castro's genuine belief in communism was not at the root of the rapid deterioration in U.S-Cuban relations

With that said, Castro certainly was a nationalist. One need look no further than the Program Manifesto of the July 26th Movement to understand why the relationship between Cuba and the U.S quickly soured. I'm having trouble finding a free link to it, but you should be able to find it online or through a university library if you have access. The driving force behind the Revolution was a politically and (more important to U.S relations) economically independent Cuba. The latter was certainly at odds with U.S interests in the region, as U.S industries, particularly in regard to sugar and other agrarian industries, held tremendous power and market share under the Batista regime. For Cuba to become economically independent, it was necessary to seize control over the islands biggest exports, namely sugar.

Thats exactly what Castro did after taking power. He issued agrarian reform that expropriated large land holdings and also stipulated that sugar plantations could not be owned by foreign nationals. This was central to the strain in U.S relations (there is a good overview here if you want more details on agrarian reform). Remember, just a few years prior the U.S staged a coup in Guatemala largely due to lobbying by the United Fruit Company over similar agrarian reforms. U.S economic hegemony in Latin America was very important to U.S Cold War interests.

In 1959, Castro would visit the U.S and meet with VP Nixon (Castro had thought he would meet with Eisenhower). After the meeting, Nixon issued a memo to the CIA, State Department, and White House that it was foolish to try to "get along" with Castro, suggesting the U.S organize the overthrow of the new Cuban regime. Whilst Eisenhower ultimately decided against this approach (unlike JFK, however it should be noted that Eisenhower did sign off on the training of Cuban exiles) the U.S did begin to issue trade restrictions, refusing to buy Cuban sugar or export oil to Cuba as a response to Cuban nationalization of U.S industries, leading to the eventual embargo in 1960. This resulted, as you have noted, in Castro turning to the Soviets to export sugar and import oil.

So to answer you question: its hard to say the U.S " forced" Castro into anything. Judging from his actions, his association with communism is of little consequence. Rather, Castro's nationalism was at odds with U.S "soft" imperialism in Cuba. Eisenhower was initially willing to work with Castro until Castro's reforms directly threatened U.S interests and influence in the region.

My understanding of this is largely from a U.S historians perspective. I hope someone with a little more expertise on the matter can fill in the gaps and details I may have missed.

EDIT: Formatting and stuff