Final answer:
The construction of the Berlin Wall is the most likely event from the provided options to have occurred between 1960-1963, symbolizing the height of Cold War tensions.
Step-by-step explanation:
Between 1960-1963, the most likely event that occurred from the given options is that the Berlin Wall was constructed. This event is closely linked with the Cold War tensions between the United States and the Soviet Union. The Berlin Wall was erected starting on August 13, 1961, to prevent East Germans from fleeing to West Berlin and by extension, West Germany, symbolically representing the ideological divide between the communist and non-communist blocs.
The Vietnam War did not end during this period; it escalated in the later years and didn't conclude until 1975. The Civil Rights Act was passed later on July 2, 1964, after President Kennedy's assassination. However, The Beatles did release their first album, 'Please Please Me', in early 1963, but the building of the Berlin Wall is the most definitive event within the entire time frame of 1960-1963.