So the best I can do is a two-part answer on US decision-making in the leadup to the Bay of Pigs, and how success was inhibited and sometimes misunderstood:
The 1954 US-backed coup of Guatemala’s socialist Arbenz government had relied upon local support – which had materialized in the form of rebel exiles and elements of the Guatemalan military. This seemed to be a good comparator to Cuba for the Eisenhower administration – Castro’s victory was relatively new and the feeling was that there remained large-scale dissent in the Cuban countryside, which could serve to support the landings, or at the very least prevent popular support (namely regional militias) for Castro’s response to the invasion. Kennedy also approved of the CIA’s assertive, “can-do” attitude – this contrasted with the more cautious and diplomatic solution advocated by the State Department. This preference would quickly change after the fiasco of the Bay of Pigs – Kennedy felt mislead by John Foster Dulles about the chances of success after the attempted invasion.
The invasion was not necessarily intended to deliver a singular knockout blow to Castro’s regime – a contingency plan was prepared for the very real possibility that the local support was not as immediate as hoped for. This called for the exile landing force to engage in a guerilla campaign in the Sierra Escambray which would eventually build up sufficient support over the course of several months to directly challenge Havana. However, this relied on the landing taking place near an environment where such a campaign would be feasible, which was ultimately not the case; initially, the landing site was not intended to be the Bay of Pigs, but Trinidad (the Cuban city-region, not the island). Whereas Trinidad was near the Sierra Escambray (very conducive to a guerilla operation), the Bay of Pigs was located within a swampy and comparatively open environment and 80 kilometres away from such mountainous terrain.
The planning for the invasion itself was somewhat rushed – Brigade 2506, the American-backed and trained group of Cuban anti-Castro exiles, had been training in Guatemala, but under pressure from its neighbours the Guatemalan government wanted the Cuban exile force to leave by April of 1961 to take the diplomatic pressure off of Guatemala City. This, combined with the logistical issues of landing a substantial number of troops (only about 1,500 landed at in April of 1961), presented severe constraints on the scale of the planned invasion. Furthermore, the top-secret planned invasion was not necessarily unknown by the Cuban community more generally – it’s said that in Miami, the invasion was a common topic of conversation in restaurants and bars. Because of this difficulty in obtaining deniability, American willingness to provide overt support was limited.
In the course of the actual invasion, US activity was impeded by an unwillingness for the CIA to communicate openly with the Pentagon, which severely undercut the efficacy of air support and logistical assistance. As it originally existed under the Eisenhower Administration, the invasion plan called for extensive naval and air bombardment of key strategic sites. The naval element was deemed too difficult to deny in the case of failure and thus was scrapped, and the aerial commitment was continuously decreased in the year prior to the invasion, partially in light of the shooting down of a U2 reconnaissance plane over Soviet territory in May of 1960. Kennedy in particular was hesitant to risk exposing direct American involvement, and thus the main complement of air support was intended to be provided by Cuban exile airmen flying ‘sanitized’ B-26s mocked to look like defectors from the Cuban Air Force.
The aerial element of the plan really was central to the success of the invasion, as this would allow the relatively undermanned Brigade 2506 to successfully establish a beachhead, or alternatively get to an area where they could carry out a guerilla campaign. While the original plan called for dozens of B-26s to carry out a number of sorties, eventually only nine (eight operation and one completing a deception flight to Miami Airport to maintain the appearance of defecting airmen) were supplied to the Brigade. Covertly, the CIA also deployed three B-26’s marked as Cubans to fly inland and cause confusion, although these would later be fired upon by the anti-Castro forces when they strayed too close to the Bay. Five of Brigade 2506’s B-26 medium bombers were shot down, a disastrous result which confirmed Kennedy’s decision to cancel a second wave of strikes, essentially leaving the landing force exposed to Cuban airstrikes, which quickly followed.
So all in all, the prospect of a large-scale Cuban uprising was seen in relation to the ability of anti-Castro forces to quickly establish a victory, or at the very least gain a foothold in Cuba, to present a challenge to Castro’s government. Once a state of guerilla (or civil) war could be achieved, then further resources could be poured into these efforts by Washington. However, the particular historical circumstances of 1961 (Guatemala forcing the invasion to take place on an accelerated scale, Kennedy’s hesitancy to expand an American commitment) resulted in Brigade 2506 landing with minimal support, thus reducing their prospect of success. Once it became apparent that the exiles had no prospect of victory, American support evaporated altogether, and Castro’s regime in Havana appeared stronger to the Cuban populace by decisively repelling a foreign-backed attempt to throw a counter-coup.
Sources:
Politics of illusion: the Bay of Pigs invasion reexamined by James G. Blight and Peter Kornbluh (1998)
Kennedy's Wars by Lawrence Freedman by Lawrence Freedman (2002)
US Foreign Policy Decision-Making from Truman to Kennedy: Responses to International Challenges by Alex Roberto Hybel (2014) – Ch. 5 particularly
The most dangerous area in the world: John F. Kennedy confronts Communist revolution in Latin America by Stephen Rabe (1999)
Red Heat: Conspiracy, Murder and the Cold War in the Caribbean by Alex von Tunzelmann (2011)
Edit: inconsistent naming of the Sierra Escambray