Kylie Bunbury stars in the Fox series”Pitch.” (Tommy Garcia/Fox via Associated Press)

Ginny Baker made history as the first female MLB pitcher when she took the mound for the San Diego Padres last month — or so one radio listener in Canada thought when she mistook the Fox show “Pitch” for reality.

“No, that’s a TV series,” CAM-FM host Lukas Banack corrected the woman who called to complain about the lack of news on Baker’s first go with the Padres after the show premiered Sept. 22. “They’ve done a great job promoting it … but it’s just a TV series.”

The baseball insiders who have successfully worked to make Baker, portrayed by actress Kylie Bunbury, believable say the story could move from fiction to real life sooner than expected.

“I think it’s aspirational, but is that a realistic possibility? I personally think so,” Chris Tully, MLB’s executive vice president of media, told The Post this week of the prospects of a female pitcher making it to the big leagues.

The story needed to be realistic for MLB to sign on to executive-produce the show, Tully said. It’s the first fictional project the league has helped produce since “Moneyball,” the 2011 film starring Brad Pitt.

“We view scripted entertainment, whether it’s television or movies, as being an extension of our efforts to find platforms on which to connect to existing fans or to reach new fans,” Tully said. “In terms of what attracted us to this particular project, well, the stars kind of aligned.”

Tully said that, because of the longstanding relationship between the league and the network, MLB was immediately interested when Fox approached with the show. But there were a few requirements the project had to meet before MLB would move forward.

One of the most important was for the plot be authentic, and in this case — thanks to headlines made by Little League pitching phenom Mo’ne Davis in 2014 — the idea of a female MLB prospect didn’t seem far-fetched.

“I think [the plot] reinforces a pre-existing notion that … all the teams from the various communities around the globe that enter teams into the Little League World Series are doing so to win and they’re putting their best available players out on the field,” Tully said. “The same is true with Major League Baseball. It’s right in line with the idea of authenticity.”

Molly Knight — a former ESPN reporter who works as a consultant with the show to ensure the plot stays true to the majors — agrees, although it took some convincing to bring her aboard.

“When I first heard about the plot, I’m like, ‘Okay, what?’ ” she said. “I’m a hardcore feminist, nothing against our gender, but just the way that we’re built physically, throwing a ball at 95 miles per hour is not realistic.”

But that’s not what Baker does. Baker doesn’t rely much on fastballs; she instead focuses on screwballs, a trick pitch that Knight says could one day land a woman on an MLB roster.

Former MLB reliever Gregg Olson taught Bunbury to pitch, training with her three times a week during production, according to ESPNW.

Knight said current MLB players she’s spoken with about the project believe a player like Baker could make it to the big leagues in real life.

“What I like about this show is she is not like some superstar phenom that comes up and mows everyone down. She’s just called up to replace an injured fifth starter and she’s just trying to hang on and she’s bad in her first start out. She’s awful,” Knight says. “She’s just trying to tread water and keep her spot, which I think is the reality. … Most of these guys that get their chance and get called up, they don’t know if it’s going to be their only chance, if they’re going to get sent back down [to the minor leagues] the next day and never given another shot.”

Even the details of the set design are true to life. Knight says the show’s replica of the the Padres clubhouse almost unnerved her.

“The first time I set foot in there, I was freaked out. I felt like I should have my reporter’s notebook,” she said. “Everything — the lighting, the temperature, even the huge Costco-sized Listerine bottle they have in the fake bathroom. It was eerie.”

Viewers can thank MLB for that. One of the stipulations the league had going into this project was that it not only be authentic in the telling of the story but also in the visuals. When possible, the show filmed at real MLB stadiums, including the Padres’ Petco Park and Los Angeles’s Dodger Stadium. It uses real MLB logos and team names. Other scenes are filmed on sets, some of which Knight helped create. On her suggestion, for example, the show’s production staff built a replica of the stadium’s family room, where the players’ wives and children watch the games.

Sportscasters and journalists appear in the show, including Fox Sports’ Colin Cowherd, Joe Buck, Katie Nolan and John Smoltz.

“We had to get the baseball right,” executive producer Kevin Falls told the Los Angeles Business Journal last month. “What really helps make this work is that you see the teams, the stadiums, you hear the broadcasters, all the genuine reference points [that] fans are familiar with. To miss on all of that would end up being a distraction and drag the whole thing down.”