The Broadway musical can seem as oldfangled as the founding fathers. But an audacious hip-hop retelling of the life of the nation’s first Treasury secretary lands on Broadway on Monday poised to become the rarest of theatrical phenomena: not only a hit, but a turning point for the art form and a cultural conversation piece.

The show, “Hamilton,” arrives with a powerful tailwind. It has already brought in $27.6 million, with just over 200,000 tickets sold in advance — huge numbers for Broadway, and among the biggest pre-opening totals in history. An Off Broadway production of the musical, based on Alexander Hamilton, which ran this year at the Public Theater, was a critical darling that sold out 119 performances, attracted a who’s who of cultural and political figures, and collected a trophy case of awards. And the show’s creator, a 35-year-old New Yorker named Lin-Manuel Miranda, has already won a Tony and a Grammy for an earlier show he had begun while still an undergraduate.

Thus far “Hamilton” has been seen by relatively few people — a total of 34,132 seats were available over 15 weeks at the Public, fewer than at a typical Yankees home game, and there remain uncertainties about how it will be received by broader audiences over time.

“The question we have to answer is: ‘Will the word of mouth be as good, or better, on Broadway? Will we measure up?’ ” said the show’s lead producer, Jeffrey Seller, who has won Tony Awards for the groundbreaking musicals “Rent” and “Avenue Q” and Mr. Miranda’s debut, “In the Heights.”