In a milestone, women outnumber men this year as directors at the Tribeca Festival. Three of them shared their paths to the director’s chair.For the director Olivia West Lloyd, it was good, old-fashioned networking that earned her the chance to make her first feature, “Somewhere Quiet.” With no film school on her résumé, she took every bottom-rung job she could get on a production set, and then connected with other peers on their way up, building a team ready to seize the moment when the opportunity to make a movie together came around.Gabriella A. Moses, whose first directing feature is “Boca Chica,” credits the film industry itself, and her participation in fellowships designed to give women and other newcomers a leg up, for getting noticed by the “right people” who offered the chance to helm the project.Maggie Contreras, the director of “Maestra,” said that she got her break from male colleagues who had already found success in the movie business and decided to give a woman they trusted a chance. Now she is making it a no-excuses priority to bring other female filmmakers along.No matter how women are getting the chance to direct these days, the sentiment that they need to lead a new generation of female filmmakers seems to prevail. All three directors, whose films are showing at the Tribeca Festival, gave key jobs — as producers, writers, designers and editors — to other women.The momentum to put more women in top positions manifests itself in a milestone this year. For the first time, the festival, which runs Wednesday to June 18 in New York City, will have more women than men vying for prizes. A considerable 68 percent of all competition films were directed by women, according to the festival.Jennifer Kim in a scene from “Somewhere Quiet,” a thriller directed by Olivia West Lloyd. Her character, Meg, is trying to readjust to normal life after a heinous abduction.Conor MurphyThat is not to say that women have achieved parity in the industry overall. Female directors remain far behind men at the top, according to a study published in January from the Inclusion Initiative at University of Southern California’s Annenberg School for Communication and Journalism. Male directors outnumbered women 11 to 1 when it came to the 1,500 highest-grossing films from the last 16 years.Stacy L. Smith, who founded the Inclusion Initiative and led the study, called that tally “abysmal.”“It doesn’t reflect the proportion of women and girls in the U.S. population nor in the world,” she said. “It’s not related to the proportion of girls and women studying in higher education. And most certainly, it doesn’t represent or reflect the number of girls and women enrolled in film school around the country.”Ms. Smith said the problem was with film company executives who failed to see women as viable directors on high-profile, big-budget films — particularly action films, which tend to do best at the box office. The playing field was more even on smaller projects, she added, and those are what make it to the rosters of film festivals, such as Tribeca.“I think that many of the institutes and film festivals have really started a concerted effort to think more critically about how they select, and who the committee is for selecting films, because we know that is where bias comes in,” she said.But the news from Tribeca suggests that a more equitable future is possible, particularly because its roster relies heavily on newcomers likely to continue creating films.How any woman makes it to the director’s chair is a personal story, of course, that starts with her own skills and ambition, but the aforementioned directors show how some women have cut a path and did it across genres.Ms. Lloyd carved out a niche in the horror/suspense category, where relatively few women are working. “Somewhere Quiet” is a tense, claustrophobic thriller set in a remote cabin in the woods. Viewers are kept guessing whether the tormented lead character Meg (Jennifer Kim) will make it out alive.“I love horror,” said Ms. Lloyd, who also wrote the screenplay. “I have since I was a teenager.”Ms. Lloyd, who has carved out a niche in horror and suspense, also wrote the screenplay for “Somewhere Quiet.”Emma HannawayShe said she believed that getting the film made was “fated in a way.” The deal was cut during the coronavirus pandemic when projects with small casts and closed locations were in demand. But she also had the pieces in place to make it happen.During her stints as a production assistant, she bonded with Taylor Ava Shung and Emma Hannaway, who were building careers as producers. “We would just talk at length about movies, and how we wanted to make movies, and what we would prioritize when given the opportunity,” Ms. Lloyd said.They were ready to go when they saw an opening, tapping their own advice network that included the producer Mollye Asher, whom they met assisting on the Oscar-winning film “Nomadland,” and her partners, Derek Nguyen and Mynette Louie.“They were super helpful in just introducing us to other production companies and getting us in touch with various people who could actually come on and make the movie,” she said.Ms. Moses’ first feature took her in a different direction, to the Dominican Republic, for “Boca Chica,” a drama about 12-year-old Desi (Scarlet Camilo), who works in her family’s beachfront restaurant but dreams of becoming a singer. The film’s intimate moments and lively music underscore its exploration of issues like human trafficking and sex tourism.Scarlet Camilo in “Boca Chica,” which features a Spanish-language script.Selene FilmsThe director had other plans for her career, envisioning herself writing and directing her own movies. To get there, she attended the Tisch School of the Arts at New York University and began seeking mentorships designed to bolster young filmmakers. She received support from the Sundance Institute, New York Women in Film & Television, and others.In 2018, she participated in the Tribeca Institute’s Through Her Lens program for rising female filmmakers and used its resources to make the short “El Timbre de Tu Voz.” After completing that project, she began lining up what she assumed would be her first feature, a story she wrote called “Leche.”But her early work came to the attention of the producer Sterlyn Ramírez, who approached her about directing “Boca Chica,” which featured a Spanish-language script written by Marité Ugas and Mariana Rondón.“It was actually through this institute, and the never-ending grant-writing and fellowships, that the producer on ‘Boca Chica’ found me,” she said.Accepting the job was a tough decision. Ms. Moses’ mother is from the Dominican Republic, but Ms. Moses herself was born in the United States and her own Spanish was lacking. Still, the movie’s themes echoed her own artistic goals and she decided “to go along for the ride.”“It was a sink-or-swim situation where I was like, ‘OK, it’s hard to make your first feature no matter what. It’s going to be even harder to do it in another country and not in your mother tongue. And it’s going to be deeply personal and probably more emotional than anything to do it in your mother’s country,’” she said.With her first feature making the cut at Tribeca, she is turning her attention back to “Leche.”A still image from “Maestra,” a documentary about female orchestra conductors directed by Maggie Contreras.Isabelle RazavetWith “Maestra,” Ms. Contreras stepped sideways into directing. She had worked extensively as a producer, collaborating with the documentary maker Neil Berkeley. She first took him the idea of directing a film about an international competition for female orchestra conductors after hearing a report about it on NPR.Mr. Berkeley surprised her by suggesting that she direct it herself. “It was as simple and profound as that,” she said.The job came with challenges. She saw her own situation as a first-time director mirrored in the women competing for a spot on the podium: They were trying to break into a profession historically dominated by men. She decided she needed to pass on the baton, so to speak, to other women.“From Day 1, I said we would have at least 80 percent women behind the cameras making this film,” she said.Ms. Contreras put together a female-led crew for “Maestra.”Ryan Musick“Maestra” follows the several conductors leading up to the charged competition, with interviews in the United States, France, Poland and Greece. In some of those places, it was difficult to find female workers, Ms. Contreras said. With a tight schedule and budget, there was pressure to fill jobs with men. She held firm to her quota.Ms. Contreras credits the female-led crew for the project’s success. Her subjects open up, telling tales about child abuse, discrimination and body insecurity. “Because of my own experiences as a human being, as a woman with my own thoughts and fears and struggles and joys and the way I show up in the world, we were able to have a conversation,” she said.That perspective, she said, echoes other arguments for giving women more opportunities: Diverse directors expand the possibilities of storytelling, which is the heart of filmmaking.Her next directing project centers on an “Erin Brockovich” type who triumphs, though in a different context from classical music. She plans to keep the same philosophy when assembling an inclusive production staff.“It’s now my responsibility to hire people who will then hire other people,” she said. “That chain cannot be severed or we go backwards.”Ms. Smith, whose academic research has made her a leading proponent of equity in the film business, said that chain affected the experiences of audiences, as well as the careers of female filmmakers.“If you have a female director, you’re more likely to have a whole series of things,” she said. “More female-driven story lines, more women over 40 in films, more women working behind the camera, and more people in below-the-line crew that are women.” More