Back in Cuba, Jorge Gomez had a lot of time on his hands. During the early ’90s when, he recalls, there was “no work, no food and no hope,” the pianist turned to music. All day.

“In Cuba, most of the time you don’t have anything to do,” Gomez says from his current home in Miami. “So, you rehearse from 9 a.m. to 9 p.m. looking for some hope. Nothing happens with your music, but you become a great musician. I only focused on rehearsing and finding a way to leave.”

When he did flee Cuba in 1995 at the age of 25, the classically trained, street-influenced performer wanted to establish a band but wasn’t finding much interest. People respected his talents enough, but their pursuit of paying gigs kept them from collaborating. After all, there isn’t an audience in America for the type of salsa-like, Afro-Cuban dance music Gomez longed to assemble. At least that’s what he was told.

“People said, ‘Are you crazy? Timba, here? Nobody knows about timba!’ The only thing I knew for sure was that I could do it better.”

And, of course, he went on to do just that.

Today, after performing alongside such monumental Cuban figures as Celia Cruz and Albita Rodriguez, and having founded one of Miami’s brightest and biggest musical exports, Tiempo Libre, it’s a different story from when he was flooded with naysayers. Already two acclaimed albums deep, Arroz Con Mango and Lo Que Esperabas, and a third album that merges classical pieces by Bach with Cuban party-flavors set to hit shelves in May, Tiempo Libre has been forging new ground for a modern brand of timba unconventionally birthed outside of Cuban soil. Needless to say, as the band’s musical director, Gomez is the one turning down offers these days.

“When I started doing music it was difficult because nobody wanted to work with me,” he says. “I didn’t have too much work to offer, so they said, ‘Oh, you are my friend and the music is incredible, but I need to pay my bills. And right now, it’s totally shifted. Now all my old friends ask me to do music with them but I have to say, ‘I’m sorry, I have new musicians already.’”

Those new musicians, all six of them, round out his twice-Grammy-nominated ensemble that, since 2001, has been translating the Cuban traditions of son, cha-cha-cha, and rumba, with Latin jazz, funk, African percussion, and their newfound American influences and immigrant experience in Miami—a place Gomez viewed as heaven upon first arriving. “[Miami’s] like Cuba except there is everything here,” he says.

Whereas in Cuba, typical timba bands are massive 18-piece ensembles whose furious polyrhythms are layered atop extensive lyrics, Tiempo Libre operates with half the members and cuts down the lyrics, but makes up for it by dishing out varied styles and combined expertise that mound into a sound just as massive—and infectious. Tinges of hip hop and rap get immersed in the band’s tight horn section and thick, torrential beats, and the only time you’ll find yourself sitting down at a show is when you’re too tired from dancing.

In response to an old, restrictive system in Cuba that wouldn’t reward him, and to those in America who didn’t believe in him, Gomez has found in Tiempo Libre the last laugh, because for a band whose Spanish moniker means ‘free time’—it doesn’t have any. These days, Gomez and his cohorts are happily hard at work making sure their international audiences are the ones hard at play.

“It’s a party not a concert,” he says. “Feel yourself in another world. Feel the music the way you feel American music, like rap or pop. If you can dance to Michael Jackson, you can dance to me.”