First things first: “Girl Shakes Loose,” the new musical by gifted composer Imani Uzuri and playwright Zakiyyah Alexander, is a remarkable achievement.

Even with the usual nervousness associated with a world premiere night, director MayAdrales’ polished production flowed smoothly Thursday at Penumbra Theatre.

Aided by Kathy Maxwell’s cityscape video projections, Karen Charles’ playful choreography and a hardworking, entertaining cast led by Alexis Sims as the title character, Adrales’ staging transports us into the propulsive story of a young woman’s wanderlust.

“Girl” is a coming-of-age show that expands the meaning of that phrase. A millennial from small-town Georgia who earned a graduate degree and founded a start-up in the Bay Area, Girl (as she’s called throughout the show) is having a quarter-life crisis. She fell in love with a woman, Ella (Tatiana Williams), but her business failed and, fearing commitment, she runs away to New York in hopes of a fresh start.

The show is partly told through flashbacks. A death in the family calls her back to the family seat in Georgia, forcing her to confront her estrangement from her mother and, eventually, Ella as well.

Uzuri’s music is a pastiche of styles celebrating African-American music. There’s ’50s R&B, ’60s soul, jazz and blues as well as rap, gospel and house. Memorable numbers include the operatic “Soymilk” — sung by Girl’s hilariously annoying vegan landlord (China Brickey) — the Alicia Keys-style piano power ballad “You Keep Saying,” and “Overqualified Black Girl,” a shimmy-shaking vaudeville number. Pianist Sanford Moore leads a tight band that gives the show its many colors and a bigger sound than its four pieces would suggest.

The script is suffused with the poetry of Sonia Sanchez, a high priestess of the Black Arts Movement whose fiery and erotic work has been seamlessly integrated into the narrative.

Even so, the show exhibits some of the challenges associated with a first-time musical, including a narrative that could be wound more tightly. The songs, as lovely and affecting as they are, don’t always arise at moments of tension when mere speaking doesn’t suffice. And the stakes for Girl are not as high as they could be.

The fact that we care about the title character — and the show, for that matter — has less to do with the slight story than the sweetness of the music and the talented cast. Sims, a New York actress making her Twin Cities debut here, imbues Girl with openness and charm, even if we don’t always feel her emotions deeply. And her gorgeous voice holds its own among some powerhouse singers.

The mostly local ensemble offers talent discoveries as well. John Jamison proves himself a versatile, showstopping performer whose characters include a flamboyant commune leader. Brickey shows range as well, delivering with operatic chops. Williams, who was Belle in “A Christmas Carol” at the Guthrie, is a fierce presence. And although Kory Pullam’s diction is not always clear, he has charisma to spare.

The cast is anchored by veteran performers Jamecia Bennett and Thomasina Petrus, who play Girl’s great aunt and mother, respectively. Both sang with the passion that we’ve come to expect from them as they lent their souls to a show that, despite the nits, adds new energy and light to the American musical theater canon.