Sometimes the best musicals can spring from the most unlikely source material. Wim Wenders’s 1999 documentary Buena Vista Social Club is a glorified concert film, featuring onstage and in-studio performances by veteran Cuban musicians supplemented by interstitial interviews with roughly a dozen different artists. American guitarist Ry Cooder and his percussionist son headed to Havana in 1996 to gather as many of these old-time musicians as they could find and recorded more than a dozen tracks over the course of six days — producing a hit album that would spark new interest in the lilting melodies, rhythms and harmonies of Cuban music.

That music — sometimes joyous, sometimes dolorous — is at the heart of director Saheem Ali’s rapturous stage musical Buena Vista Social Club, which opened Wednesday at Off Broadway’s Atlantic Theater Company in a production that is begging for a longer, bigger life. Ali achieves something close to perfection in adapting the film, starting with an affectionate re-creation of classic tunes with a 15-piece onstage band. There are 15 songs in all, about half pulled from the album and film, executed with polish and panache.

But Ali’s real contribution, what makes the music come alive as theater, is his introduction of dance and a narrative structure that together illuminate volumes about the evolution of Cuban society. The choreography, by Patricia Delgado and Justin Peck, is an artful mix of Afro-Cuban, ballet and ballroom styles that elevates the syncopated rhythms of the score while allowing for individuality that’s further accentuated by Dede Ayite’s costumes. (Full credit to the dancers: Skizzo Arnedillo, Angelica Beliard, Carlos Falu, Hector Juan Maisonet, Ilda Mason and Marielys Molina.)

Book writer Marco Ramirez has smartly gone beyond the thin storytelling of Wenders’ documentary to focus on a handful of performers and their before/after trajectory from their start in the pre-Castro 1950s to their reunion for this 1996 album. The dual timelines provide a strong narrative thread for the show, with a special emphasis on the diva-like chanteuse Omara Portuondo, who appears only briefly in the film and here becomes a character that recalls both Ma Rainey and Effie in Dreamgirls. Natalie Venetia Belcon is astonishing in the role, with a powerful voice, an earth-mother presence and a face that speaks volumes about the sacrifices she made along the way. We also meet the younger version of Omara (Kenya Browne), who gets her start performing with her sister Haydee (Danaya Esperanza, a vocal powerhouse) in tourist hotels like the Tropicana — where darker-skinned singers like Ibrahim Ferrer (Olly Sholotan) must perform under the stage, unseen, if they are allowed to perform at all.

Omara, who comes from a well-bred family, finds herself drawn to the pure music-making of lower-class venues like the Buena Vista Social Club — where she sparks to the energy of kindred spirits like singer-guitarist Compay Segundo (Jared Machado, who exudes charm) and pianist Rubén González (Leonardo Reyna). These ’50s-set scenes pulsate with the energy of creative minds at play in each other’s company — though the threat of change looms with references to stashes of illegal rum and weapons. When revolution breaks out, Haydee flees to Florida and urges Omara to join her: “The world is on fire and you’re singing pretty songs.” But Omara holds firm, to her people and to her music, a rawer, less refined version of the tunes she had been performing for tourists on the Tropicana stage.

Ali also tracks the parallel story of the 1996 making of the album. Leonardo Reyna’s Compay is a still-spry gentleman with quick fingers on the guitar, Ibrahim (Mel Semé) is busking on the Havana boardwalk to make ends meet, while Rubén (Jainardo Batista Sterling) has dipped into dementia. Their country and their culture may have moved on, but their music has not. It’s the one thing that continues to sustain them, and to bind them when an academic-minded producer from America (Luis Vega) seeks to corral them back into the studio to record their best work from the past. Remarkably, this is the rare show that succeeds despite the fact that the songs are not used (or adapted) to try to advance the plot — they set a mood, or underscore a feeling, or serve as pure performances unto themselves.

Somehow, it all works. The dual-timeline story, the seamless integration of song, the natural introduction of movement, the way that the lyrics convey feeling and sensation even to those (like me) who don’t speak Spanish. Arnolfo Maldonado’s two-level set design and Tyler Micoleau’s lighting smartly eschew Broadway glitz for the softer, worn-down colors and tones of old Havana. You can almost smell the mariposa and stale cigars. Buena Vista Social Club salsas and rhumbas to the front of the line as the best new musical of 2023.