Janelle Monáe, left, Taraji P. Henson and Octavia Spencer in “Hidden Figures.” (Hopper Stone/SMPSP/Twentieth Century Fox)

The stars of “Hidden Figures” trickled in recently for a group interview at a Washington, D.C. hotel. The first to arrive was Janelle Monáe, with a red beret and gold strands threaded through her braids. Then Octavia Spencer walked in.

“Don’t you look like Queen Nefertiti?” Spencer said to the perfectly coifed Monáe.

Taraji P. Henson appeared last, and her co-stars greeted her — and her cropped, backless sweater — with “oohs” while clapping their hands.

The women had just been nominated for best ensemble in the Screen Actors Guild Awards. Spencer had also been singled out for her supporting role, though she played down that individual achievement.

“Any upward movement for one of us is upward movement for all,” Spencer said. “If we don’t get there together, we don’t get there.”

The spirit of teamwork also shows up in the plot of their movie, which came out Sunday. During the space race, NASA’s Langley Research Center employed black female mathematicians to calculate, among other things, launch and landing for the country’s first astronauts.

After all, John Glenn didn’t make it into space alone, and one person who helped was Katherine Johnson, played by Henson. Spencer and Monáe play two other real-life math virtuosos, Dorothy Vaughan and Mary Jackson.

During that era, black working women had few opportunities beyond becoming nurses or teachers, so the women faced a lot of discrimination to help their country beat the Soviets to the moon. The human “computers” found solidarity as they worked together at a place that had segregated bathrooms and lunch tables.

That was the kind of discrimination that director Ted Melfi was interested in exposing. We’ve seen water fountains marked “whites only” on-screen before, he said, not to mention civil rights activists getting hosed down or tear-gassed by the police. But how about the more insidious institutional prejudice?

“That’s the racism we have today — the unconscious bias,” he said. In the movie, after Katherine begins working in an office with only white men, a coffee pot marked “colored” appears — and she doesn't know who did it.

“You can’t really point a finger,” Melfi said, because the problem is the whole system, not a single person.

Unconscious bias has also been a topic of discussion about Hollywood. Unlike earlier this year, there will undoubtedly be actors of color up for Oscars come February. But that doesn’t change the fact that very few movies focus on characters who are women or minorities.

“I remember a time when Whoopi Goldberg was the lead actress in Hollywood, and I don’t see that replicated right now,” Spencer said. “I don’t know what happened and why they stepped away from seeing black women as leads.”

Echoed Henson: “There’s still work to do, but you can’t let it make you bitter. You just have to keep doing the work.”

The women also found their characters instructive in some ways.

“What I loved about all these women is that they did not allow the obstacles to deter them,” Monáe said. “They kept strong mentally, they let the work speak for itself, and they were focused on the future.”

Henson, flanked by Spencer and Monáe, as their characters meet John Glenn. (Hopper Stone/SMPSP/Twentieth Century Fox/Hopper Stone/SMPSP/Twentieth Century Fox)

Some producers and studios appear to think that casting actors of color is some huge gamble, but producer Donna Gigliotti isn’t one of them.

As soon as she saw the proposal for the original book by Margot Lee Shetterly (which came out in September), she knew she had to make the film, and she wanted to make it fast. Spencer came aboardfirst, though when she heard about the story, she thought it must be historical fiction. She, like most people, knew nothing of the women at NASA.

Pharrell Williams, a producer on the drama who also worked on the score, followed shortly after. He had to be involved, he said, because the story combined so many things he loved: his native Virginia, NASA and women.

“Here were three African American female protagonists who weren’t necessarily divorcées or consoling each other or going away for a girls’ getaway,” he said recently. “This was three African American female protagonists who were technologically advanced.”

Melfi, meanwhile, found himself at a crossroad. He wanted to direct the project, but he was a finalist to direct Marvel’s newest iteration of “Spider-Man” — a surefire global megahit. He asked Gigliotti if perhaps she’d be open to pushing back the filming of “Hidden Figures.”

“And I said to him, ‘Please, would you leave my office — are you kidding me?’ ” Gigliotti recalled a few months ago. “He had a couple of sleepless nights and he told his agents to take him out of the running for ‘Spider-Man.’ ”

He still got to film some superheroes, as far as Gigliotti’s concerned. These ones just have more earthly powers.

“Hidden Figures” stands out in many ways from other awards hopefuls. Almost all of them are about people in mourning, most of whom are men. Even the joyful “La La Land” has a bittersweet streak. But “Hidden Figures” has a completely different feel. With a soundtrack of buoyant, retro tunes by Williams — not to mention a Golden Globe-nominated score he worked on with Hans Zimmer and Benjamin Wallfisch — the movie bubbles with energy and optimism despite some of the difficult themes.

It may not get quite as many moviegoers as Marvel’s next blockbuster, but with its SAG and Golden Globe recognition, prospects are looking good that the Academy Awards will show “Hidden Figures” some love, too.

It took a team to get there. Spencer compared Henson’s remarkable lead performance to Atlas carrying the world on his shoulders. But Henson dismissed that before heaping praise on the women around her and the crew who helped make the movie a reality.

“We’re about to prove that black women can open a film,” she said, making a big circle with her hand that seemed at once inclusive and decisive.

Hidden Figures PG. At area theaters. Contains some mature thematic elements and brief coarse language. 127 minutes.