It would seem a daunting challenge to craft a feel-good musical set in Cuba in 1956, the year that Fidel Castro returned with his comrades to begin their insurgency in earnest, and 1996, as the country was reeling after the collapse of the Soviet Union. Yet both the resilience of the Cuban people and their artistic contributions are being celebrated in a new Broadway show with irresistible exuberance, not to mention staggering talent.

“Buena Vista Social Club” actually began its life as a Grammy Award-winning album produced by American guitarist Ry Cooder; it was followed by a film documentary directed by Wim Wenders. Mr. Wenders used interviews and performance footage showcasing the titular collective, named after a Havana club that had flourished before the revolution and featuring mostly Cuban musicians, some of whom had essentially been retired when Mr. Cooder recruited them.