The fingerprints of the film industry are all over the new Broadway revival of “Sunday in the Park With George.” There’s star Jake Gyllenhaal, for one thing. And there’s the unheard-of speed with which the show came together: The production at the newly refurbished Hudson Theatre was announced in mid-December, and previews began Feb. 11.

“The film world is a little more fly by the seat of your pants,” says Riva Marker, president of Gyllenhaal’s Nine Stories Productions and a producer on “Sunday.”

The revival of Stephen Sondheim and James Lapine’s musical, which also stars Annaleigh Ashford, began life as a three-day concert staging in October for New York’s City Center. It wasn’t supposed to go beyond that. But when “Burn This,” the play in which Gyllenhaal was to have starred for the Hudson’s reopening, fell through, Broadway found itself with a movie star and a venue available at the same time. Marker, composer Jeanine Tesori, and Hudson Theatre owner Ambassador Theatre Group jumped.

“The way this thing came together, it felt almost like fate was pushing for it to happen,” Gyllenhaal says.

Although he made his Broadway debut in the 2015 play “Constellations,” “Sunday” marks the first time Gyllenhaal will be singing. But don’t hold your breath for a Tony: The show ends its run April 23, before nominations are announced, so the producers decided to withdraw it from consideration. “These awards are partially about getting attention and making sure people see shows that are still running,” Gyllenhaal notes. “There’s no reason to usurp any of that.”

Now that movie musicals are having a moment, it seems logical to ask which one he’d want to star in. “I’ve never been someone who goes, ‘I wanna do that.’ But at some point, Tevye would be really great,” he says, referring to the lead in “Fiddler on the Roof.” “I’m working on the beard, obviously.”