There has never been a movie quite like “Emilia Pérez,” so it’s fitting that its star, Karla Sofía Gascón, is one of a kind, too.

In the film from director Jacques Audiard, Gascón plays a Mexico City cartel kingpin who fakes death in order to transition abroad in secret. Years after her gender-affirming surgery, the newly rechristened Emilia contacts the lawyer who helped arrange it (Zoe Saldaña) and has one more request: a reunion with the unsuspecting wife (Selena Gomez) and children she left behind, even though returning to the scene of her old crimes could have dire consequences.

The multitude of genres suggested by this synopsis — a gritty drug-world exposé, a family melodrama, a trans-empowerment narrative — are further complicated by the fact that “Emilia Pérez” is a musical, meaning the characters are liable to break into song, whether they’re in a love scene or clashing in a heated gunfight. In a film full of big swings, it’s hard to imagine any of the wild ideas holding together if it weren’t for Gascón, who can contain all of those multitudes in a single freighted look. Many pundits believe that after Netflix releases “Emilia Pérez” in November, Gascón will make history as the first openly trans actress nominated for an Oscar.

In May, Gascón, 52, was the breakout star of the Cannes Film Festival, where “Emilia Pérez” won a best actress award that was shared among all the movie’s leading women. Since her castmates had returned home before the awards ceremony, an overcome Gascón took the stage on their behalf, and her emotional speech was the night’s highlight. At the microphone for nearly six minutes, Gascón flitted between Spanish and English as she tearfully asserted the humanity of trans people, joked about bribing the jurors, paid romantic tribute to her co-star Gomez, then apologized to Gomez’s boyfriend for her ardor.

Afterward, Gascón tried to explain her speech’s breathless sprawl. “I’ve never been given a prize,” she told reporters. “I’ve mostly been given blows and kicks.”

Spanish-speaking audiences may already be familiar with Gascón, a veteran of Mexican telenovelas who starred in the hit 2013 film “Nosotros los Nobles” and transitioned six years ago while in the public eye.

“It was very difficult,” she said during a recent interview in Los Angeles. “People knew me a certain way, and then I changed, so I constantly felt that I had to justify myself. I was always fighting with everyone.”

To have her identity and transition dissected in editorials and on talk shows was a constant struggle. “When you go through those moments, you have the impression that the whole world is against you,” she said.

Gascón, speaking in Spanish with a translator present, talks with the excitement of someone who knows herself well and can’t wait to tell you what she has learned. She sometimes spoke at such length that her translator filled three pages of a legal pad just scribbling down a single story. In that way, she is quite unlike Emilia, who needs to say very little to be heard.

Most of the time, though, Gascón can’t help but recall her character. I noticed the same quicksilver shifts from gravity to levity that had proved so compelling in her performance. When I mentioned that to Saldaña on a call later, she laughed.

“I’m telling you,” she said, “there were moments in which I was like, what is the difference between Emilia and Karla?”

Audiard put it more bluntly: “I think that Emilia is Karla Sofía. I wouldn’t know where one starts and the other ends.”

Gascón has never been afraid to dream big. Born in Alcobendas, Spain, a town near Madrid, she was raised in a working-class family but felt destined for stardom.

“At 16 years old, I woke up one day knowing what I had to do — don’t ask me how,” Gascón said.

Gascón’s ambition far outstripped her opportunities — the only jobs available then were background-player gigs — but she took everything she could find and kept at it, eventually working her way up to commercials and minor TV shows. Director Julián Pastor encouraged her to move to Mexico, where she was cast in projects that required horse-riding and sword fighting. “It was full of action and adventure, exactly what I was looking for,” she said.

By her mid-40s, with several career successes under her belt, Gascón still had not yet begun to live openly as a woman, and the years spent in secret had taken their toll. “There were some very painful moments,” she said. “I even thought of taking my own life at some points.” With the support of her family, she made the decision to pursue gender-affirming surgery. Of her wife, Marisa, whom Gascón has been with since they met as teenagers, she said: “We’ve obviously shared a big chunk of our lives together, but I’ve never deceived her about who I was.”

Still, Gascón made the decision knowing it could cost her everything in the career she had worked so hard for. “When I finished my transition, I didn’t know if I was going to have a career after that,” she said.

In 2022, when Audiard, the director of acclaimed dramas like “A Prophet” and “Rust and Bone,” embarked on his casting search for “Emilia Pérez,” he found himself frustrated. Sessions in Los Angeles and Mexico City had come up empty, in part because Audiard originally conceived the character as much younger. “I realized I was wrong about the character’s age,” he said. “If they were too young, it’s as if they didn’t have a history.”

That much, Gascón had in spades. After transitioning, a diverse creative portfolio had helped her get by — Gascón has written two books and competed on a celebrity edition of “MasterChef” in Mexico — and an eight-episode role in the Netflix series “Rebelde” served to reestablish her as a performer.

Her audition earned a flight to Paris to meet Audiard, who said they formed an instant connection. “The minute I saw her, that was it,” he explained, praising Gascón’s sense of authority and playfulness.

After a screening of the film at Netflix, Gascón told me that a staffer there had praised her performance but failed to realize she also played Emilia before her transition, when the character presents as a gruff, bearded drug lord.

“I can tell you that from an egocentric point of view, I’m mad that people don’t realize it’s me playing both,” she said, “but at the same time, I feel very proud, too.”

Audiard initially sought to cast a cisgender male actor as Emilia before her transition, presuming that Gascón wouldn’t want to play that portion of the role. Instead, she fought for it.

“Now I understand why she was so interested. Because for her, playing the role of a man is an activity that requires creativity,” Audiard said. “As an actress, this is something you don’t refuse.”

Gascón knows that when “Emilia Pérez” debuts on Netflix, her trans identity will be subjected to scrutiny from a global audience. Even during her Cannes speech in May, she predicted: “Tomorrow, there will be plenty of comments from terrible people saying the same things about all of us trans people.”

Though she conceded that words could sometimes wound her, Gascón felt it was a small price to pay for personal authenticity. “I have a level of freedom that many would envy,” she said. She said she hoped that feeling of inner peace could be retained during the monthslong awards campaign about to begin.

“I am 52 years old, and at this age, I am in balance,” she said. “Other people are thinking ‘Wow, this is a special moment, you must be very nervous or very excited.’ No, I am normal. I prefer it that way.”

Whether she makes Oscar history for “Emilia Pérez,” only one thing has her truly concerned.

“What I’m afraid of,” she said, “is how am I going to be able to top this?”