The Coen brothers are not the type to shrink from a creative challenge. So for “Inside Llewyn Davis,” their wry take on the 1960s Greenwich Village folk-music scene, they wrote a virtually uncastable part.

Llewyn had to be an abrasive narcissist, yet relatable. Funny and tragic. He needed to be a fresh face, to appear in every scene and hold his own opposite Carey Mulligan, John Goodman and Justin Timberlake. And he had to perform a half-dozen folk classics start to finish. Live, on camera, thrillingly. No George Clooney “O Brother, Where Art Thou?” lip-syncing for this one.

The field of musicians who could act, and actors who could sing, was limited. “The fact of the character being a musician, and a musician that you want to watch perform, that’s a whole different talent and set of qualifications,” Joel Coen said. “Who knows if that person exists? And, you know, he did.”

The Coens found Oscar Isaac. The Guatemala-born, Julliard-trained 33-year-old fronted punk bands since his high school days in Miami, and acted for the likes of Ridley Scott (“Robin Hood”) and Nicolas Winding Refn (“Drive”).

Isaac filled the bill, all right. “Llewyn Davis” won the grand jury prize at Cannes, and Isaac is up for a best actor/comedy Golden Globe.

“It was beyond luck. I don’t know what we would have done if Oscar hadn’t walked into the room,” Joel said.

Starring in a film “was something I had wanted to do and felt ready to do, particularly with this character, a character I felt I understood,” Isaac said. “He’s someone who wants to succeed and fail in equal measure. He wants to remain true to his authentic voice, but he’s sacrificing his own happiness for an ideal. Life squeezes him. These are the noises he makes.”

Dream come true though it was, Isaac said his first experience carrying every scene in a film — particularly for the Coens, his favorite filmmakers — was “terrifying.”

“I had to put it in the back of my head. Just to focus on the task at hand, I had to in a way convince myself nobody was even going to see the movie.”

To prepare, Isaac studied voice and guitar with an old hand from the Village coffeehouse era. He worked through a week of pre-shoot recording with all the musicians and actors and producers T Bone Burnett and Marcus Mumford (Mulligan’s husband) to refine the soundtrack arrangements. His role’s great acting challenge, Isaac said, was “projecting warmth without smiling or trying to ingratiate myself, none of the regular things a person does to make people at ease or make them like him. Then people who are moved by him are moved to a much deeper level.”

The film upends the arc of typical rise-ruin-and-redemption music stories. “Llewyn Davis” shows a star not being born, a talented man whose life is a round of dull routine and unpleasant surprises. The character was very loosely based on Dave Van Ronk, a respected musician of the era who never achieved Dylan-level fame, but the idea for the film came to Joel Coen as a visual image.

“He suggested what if we start a movie with a folk singer being beat up outside Gerde’s Folk City in the Village in 1961?” Ethan recalled. What story would lead up to a fistfight outside the legendary music club? “For some reason it seemed interesting. There could be some kind of movie coming out of that.” It wasn’t until after “True Grit” that the brothers sat down and wrote the script.

The story inverts the commonplace postwar movie theme of admirable hipsters and wet-blanket squares. “It wasn’t planned,” Joel said. “There was something funny about how in that scene, how clear-cut, in a self-satisfied way sometimes, that distinction was between sellouts and squares on the one hand and authentic performers. We were kind of playing with that.”

It also tweaks some of the affectations of such folkie legends as Ramblin’ Jack Elliott, a Stetson-wearing singer who was the son of a neurosurgeon from Queens. “A lot of people in the movie are amalgams who have some relation to a person from that era,” Joel said. That would include Bob Dylan, whom the Coens somehow have never met.

“He’s always been nice to us. He’s let us use his music in a couple of our movies,” including “Farewell” at the finale of “Llewyn Davis,” “but he’s never felt the need to meet us,” Ethan said. “We’re not entertainment industry insiders.”