When Ynon Kreiz arrived at Mattel in April 2018, the newly installed chief executive had one mantra when it came to a feature film starring Barbie, a project he really wanted to get off the ground: He didn’t care if the movie sold a single additional doll.

But “Barbie” the film had to be good and a cultural event. It had to be different. It had to break molds.

And if that meant turning the chief executive of Mattel — i.e., himself — into the object of comic ridicule in the portrayal of the chief executive character in the film (“vain and foolish to the nth degree,” as The Guardian put it), then so be it.

That approach has paid off to a degree that even Mr. Kreiz could hardly have believed possible. “Barbie” is close to grossing $1.4 billion and passed one of the “Harry Potter” movies as the top-grossing Warner Bros. film of all time. It could end up near the $2 billion mark. (The record-holder is 2009’s “Avatar,” at $2.9 billion.)

How Mattel pulled off a feat that had eluded the company for years was the subject of recent interviews with Mr. Kreiz; Robbie Brenner, Mattel’s executive producer of films; spokespeople for Margot Robbie and Greta Gerwig, the film’s star and its writer-director; and others familiar with the doll’s sometimes tortuous path to the big screen.

Mattel and Warner have jealously guarded their financial arrangements. But people with knowledge of their agreement said Mattel earned 5 percent of the box office revenue, as well as a percentage of eventual profits as a producer of the movie and additional payments as owner of the Barbie intellectual property rights. At $2 billion in box office revenue, that amounts to $100 million. In addition, there are sales of merchandise connected to the movie as well as an expected boost in sales of dolls.

Representatives for Mattel and Warner declined to comment on the financial arrangements, though the company’s chief financial officer said at a conference on Thursday that the company would make about $125 million in total billings from the film.

Even though Barbie results weren’t reflected in Mattel’s latest earnings, released July 26, all anyone wanted to talk about at the earnings call was “Barbie.” Mr. Kreiz hailed the film as a “milestone moment” in the company’s strategy to “capture the value of its I.P.” and demonstrate its ability to attract and team up with top creative talent — a cornerstone of its ambitious slate of more toy-themed movies.

After the first “Barbie” trailer — showing a hyper-blond, Day-Glo-clad Ms. Robbie and Ryan Gosling skating along Venice Beach — went viral in December, anticipation started building. Mattel stock has been on a tear. It has gained 38 percent, from $16.24 on Dec. 19 to this week’s $22.30. The S&P 500 rose 8 percent over the same period.

Wall Street has been reluctant to give much credit to one hit, on the theory that such success is hard to replicate. (“Barbie” has had no discernible impact on Warner Bros. Discovery’s stock price.)

But for Mattel, the positive impact of “Barbie” goes far beyond just one film. The company’s yearslong strategy to become a major film producer, using its vast storehouse of toys as intellectual property, had been met in Hollywood with skepticism, if not outright mockery. A-list talent wasn’t lining up to direct a plush purple dinosaur like Barney. But now the perception that Mattel’s leadership is willing to trust and support an unorthodox creative team that delivered both a box office bonanza and a possible awards contender has radically altered that.

And Mattel’s surprising willingness to make fun of itself was one of the elements that mostly delighted critics and added to the buzz that roped in many more moviegoers than the “Barbie” fan base.

That Mr. Kreiz was willing to laugh at his own caricature came as something as a surprise to some acquaintances and former colleagues. An Israeli military veteran with dual Israeli and British citizenship, a former professional wind surfer, an avid kite surfer and a fitness buff, with more than a passing resemblance to a younger Arnold Schwarzenegger, the 58-year-old Mr. Kreiz comes across as more of a square-jawed G.I. Joe action hero than a Barbie fan with a sense of humor.

Mr. Kreiz’s entire career was in media and entertainment, not retail. His longtime mentor, the Power Rangers entrepreneur and billionaire Haim Saban, hired him fresh out of the University of California, Los Angeles, to launch Fox Kids Europe, a joint venture with Fox. He later ran Maker Studios, a YouTube aggregator, which Disney acquired in 2014. Mr. Kreiz left in 2016, and Maker was folded into the Disney Digital Network in 2017.

That “Barbie” even got made was no small feat. It had languished at Sony for years, with Mattel routinely renewing the option, as various writers struggled to adapt the doll for the big screen. Although one of the most popular toys ever, Barbie was the subject of intense controversy, seen both as a symbol of female empowerment and as an impossible standard of beauty and femininity. The only feasible approach seemed a parody. The comedian Amy Schumer was once slated for the part. But scripts came and went.

Weeks after becoming chief executive in 2018, Mr. Kreiz refused to renew the Sony option, according to multiple people interviewed for this article. He called Ms. Robbie’s agent and asked for a meeting. Ms. Robbie was among the most sought-after young actresses in Hollywood, fresh from acclaimed performances in diverse roles — as the ill-fated ice skater Tonya Harding in “I, Tonya”; in Martin Scorsese’s “The Wolf of Wall Street”; and as a fixture in Warner’s DC Comics universe as Harley Quinn, the Joker’s former girlfriend. And while no human could replicate Barbie’s exaggerated dimensions, Ms. Robbie came reasonably close, while also radiating wholesome beauty.

Ms. Robbie was simultaneously reaching out to Mattel and Mr. Kreiz after learning that the “Barbie” option hadn’t been renewed. She was looking for a potential franchise to take to Warner, where her production company, LuckyChap, had a first-look deal. But she wasn’t looking to star in the film herself.

Over breakfast at the Polo Lounge at the Beverly Hills Hotel, the plush entertainment and celebrity hangout not far from Mattel’s less glamorous El Segundo headquarters, Mr. Kreiz shared his vision: He didn’t want to make movies in order just to sell toys. He wanted something fresh, unconventional, bold.

“Our vision for Barbie was someone with a strong voice, a clear message, with cultural resonance that would make a societal impact,” he said, recalling his message.

Mr. Kreiz’s obvious enthusiasm and determination, and his pitch for creative integrity make him hard to resist, as Ms. Brenner, a producer, discovered when he recruited her to run the newly created Mattel film division during another meal at the Polo Lounge. Ms. Brenner, a respected producer and an Academy Award nominee for “Dallas Buyers Club,” was attracted to his idea for the movie. In Mr. Kreiz’s vision, Mattel would be as much a movie company as a toy company. The two bonded after he asked her who should play Barbie, and she, too, volunteered Ms. Robbie.

At their first meeting, Ms. Robbie suggested Ms. Gerwig for the director. The two were friends and had talked about working together. Mr. Kreiz loved the idea in part because it was so unexpected — Ms. Gerwig had directed and written acclaimed but offbeat independent films like “Frances Ha,” “Lady Bird” and a new take on the classic “Little Women,” but no big-budget fare.

“Lady Bird” was one of Ms. Brenner’s favorite movies. But would Ms. Gerwig consider such a mass-market, commercial proposal?

Ms. Gerwig, it turned out, had played with Barbie dolls and loved them. She even had old photos of herself playing with Barbie. Ms. Brenner met with Ms. Gerwig and her partner, Noah Baumbach, also an acclaimed screenwriter and director, at an editing facility in New York. They kicked around a few ideas, but nothing concrete emerged. Anything seemed possible.

A deal was struck, and Warner signed on as co-producer. Once Ms. Gerwig was on board, Ms. Robbie agreed to star.

At which point Ms. Gerwig and Mr. Baumbach retreated. “I know it’s not conventional and not what you’re used to, but we have to go into a room for a few months. That’s how we work and want to do it,” as Ms. Gerwig put it, Mr. Kreiz recalled.

When the script did land in Ms. Brenner’s email, it was 147 pages — the length of a Quentin Tarantino film, epic by Hollywood standards. She closed her office door and started reading. “It was like going on this crazy ride,” she recalled. It broke rules, including the so-called fourth wall, addressing the audience directly. It poked fun at Mattel.

New to the company, Ms. Brenner didn’t know if this would prove too much for Mattel executives. But she believed it was a great script.

Ms. Brenner’s first call was to Mr. Kreiz. “I’ve read a lot of scripts, and this is so different,” she told him. “It’s special. You don’t get this feeling many times in an entire career.”

Mr. Kreiz read the script twice, back to back. “It was deep, provoking, unconventional and imaginative,” he said. “It was everything I was hoping it would be.”

Ms. Brenner was pleasantly surprised. “Ynon is a very confident person,” she said. “He can laugh at himself.”

At one point Mr. Kreiz flew to London, where “Barbie” sets were being built at Warner’s studio outside the city. He and Ms. Gerwig spent a half-hour discussing the perfect shade of pink.

Mr. Kreiz and Ms. Brenner knew they had a potential hit. “It was our secret that we couldn’t talk about,” Ms. Brenner recalled.

The original budget target of $80 million jumped above $120 million once Ms. Gerwig was signed. But even that wouldn’t realize the director’s full vision for the film. For Warner executives it was a struggle to find what are known as “comps,” similar films that had grossed enough to justify such an outlay.

Would “Barbie” be another “Charlie’s Angels” from 2019 — which was budgeted at $55 million but grossed only $73 million and, after marketing costs, lost money? Or another “Wonder Woman” from 2017, budgeted at over $100 million, with a worldwide gross of $822 million?

Eventually the budget hit $141 million and, with some reshoots, ultimately topped $150 million.

On opening night, July 21, Mr. Kreiz took his 19-year-old daughter to the Regal cinema complex at Union Square in Manhattan. As they neared the theater, droves of moviegoers — and not just young girls — were heading to it in pink outfits. Five screenings were in progress. All were sold out.

Mr. Kreiz and his daughter dropped in and out to gauge audience reactions. People laughed, applauded and in a few cases shed tears.

Of course the success of “Barbie” has drastically raised the bar — and expectations — for Mattel’s movies in development, starting with “Masters of the Universe,” written and directed by the brothers Adam and Aaron Nee. Twelve more films are in various stages of development, including a “Hot Wheels” produced by J.J. Abrams, also at Warner. Some of these may need to be rethought.

And there will no doubt be “Barbie” sequels, perhaps even a James Bond-like franchise, which would be Mr. Kreiz’s ultimate fantasy (although he said it was too soon to discuss any such plans).

Mr. Kreiz acknowledged that in a notoriously fickle and unpredictable business, future success is hardly assured. But “Barbie” has given Mattel momentum — the beginning of what he calls “a multiyear franchise management strategy.”