CLEARWATER, Fla. — Somewhere over Tampa Bay, while driving on the causeway connecting Tampa, Fla., to here, Rachel Balkovec asked the two top Yankees prospects in the back seat of her car if they had ever watched softball.

Antonio Gomez, 20, a catcher from Venezuela, said he had. Jasson Dominguez, 19, one of the highest-ranked prospects in baseball, said he had, too — but it was men playing in his native Dominican Republic. Neither had seen women play college softball.

“You’re about to see what female athletes look like,” said Balkovec, 34.

It was during a dinner with those players that week in mid-February, long before the minor league season began, that Balkovec realized that they probably did not know much about her background.

They knew she was a unicorn — the first woman to serve as a manager in affiliated professional baseball — but they didn’t know much about softball, the sport Balkovec played in college before her winding and trying path to this point. So Balkovec, the manager of the Tampa Tarpons, a low Class A affiliate of the Yankees, had an idea: take Dominguez and Gomez to a preseason softball tournament of several U.S. colleges that was taking place near the Yankees’ spring training facility.

Balkovec’s hiring has been a watershed moment for the male-dominated sport of baseball. Countless women can relate to the rejections she received for job openings, to her building an even more comprehensive résumé as a result (she has a master’s degree in sport administration and pursued a second, in biomechanics), to her small paychecks and to her long path to running a baseball team.

She has shattered glass ceilings during her 10 years working in professional baseball: the first woman to hold a full-time position as a minor league strength and conditioning coordinator (with the St. Louis Cardinals in 2014); the first woman to serve as a full-time hitting instructor by a big league team (with the Yankees in 2019); and now the first female manager. All along the way, Balkovec has opened people’s eyes. Spending four hours of a Saturday evening taking Dominguez and Gomez to softball games was the latest example.

“I didn’t have this dazzling sports career, but I was a high-level athlete,” said Balkovec, a catcher on the softball teams at Creighton University and the University of New Mexico. “And in the Dominican Republic, for example, you just don’t see that that often with women. In fact, almost never. And they don’t get it, so I want to show them.”

Balkovec said this as she drove to pick up Dominguez and Gomez from the hotel they were staying at during a Yankees’ preseason camp. During the 30-minute drive to the site of the St. Pete/Clearwater Elite Invitational, they talked about the intricacies of softball, her early forays into professional baseball in 2012 (working as a receptionist for the equipment company Marucci in the early morning and, in the late morning, as a strength and conditioning intern for the Cardinals) and the reason for their trip in the first place.

“I came because Rachel always has good ideas,” Gomez said in English — following a rule of Balkovec’s designed to get the two players practicing their second language. (Balkovec, a Nebraska native, frequently answered in Spanish, which she learned from Latin American players over the years.)

Throughout the evening, the players learned more about Balkovec, who made her managerial debut on April 8, and about what she represented. As they rode the tournament trolley from the parking lot to the softball stadiums, Balkovec explained why she was now more comfortable hanging out with her players away from the field.

As a young strength and conditioning coach, she said she would take players to the supermarket to teach them how to eat healthy, but she would never take them to dinner. She called those days “the Wild West” because there were barely any other women in baseball. She said that people feared romantic relationships developing with the players, and that she would never wear a crop top or tank top around them.

“She’s a big picture thinker, and in any walk of life — a coach, a manager, my manager at my job — first and foremost, if you like someone and you trust them, you’re willing to do whatever they ask,” said Balkovec’s sister, Stephanie, in a phone interview. “For a long time in her early days, I used to yell at her because she wouldn’t let them see her be human.”

But, Balkovec said, as she got older, her colleagues and players got to know her better and society evolved (little by little, more women worked in baseball). She didn’t worry about how things like clothing were perceived anymore because her priorities were clear. She sees herself not only as a manager but as a life coach to her players, particularly the Latin American ones who face unique challenges. She not only talks to her players about how to improve their swings and their bodies, but she is also tough or compassionate as needed, and she speaks to them about such matters as their off-field goals and how they should respect women.

“That’s part of who Rachel is, somebody who cares a lot about these guys, and it’s not always in most traditional way, like ‘Oh, let’s go to a baseball game so we can talk about this guy’s slider’ or ‘Let’s watch video,’” said Kevin Reese, the Yankees’ vice president of player development, in a phone interview. “That’s where you’re probably going to get some fringe benefits of Rachel because she sees things through a little bit different lens of life and that has a lot of advantages.”

Immediately after stepping off the tournament’s trolley, a fan recognized Balkovec. Gomez and Dominguez laughed to themselves but were impressed.

This continued for the rest of the night. As the three bounced between the concurrent games of the University of Texas-U.C.L.A. and Michigan-Louisiana State, Balkovec was stopped at least six more times for an autograph or to pose for photos, including by a youth girls’ softball team in attendance. That happened to Gomez and Dominguez, a highly touted prospect who signed with the Yankees for $5 million when he was 16, a combined three times.

“Rachel is so famous!” Gomez said.

During the games, Dominguez and Gomez peppered Balkovec with questions or observations. They pointed out swings they liked. They cheered after big plays. (At one point, Gomez joined the Texas fans’ chant.) They snapped photos and took videos of the game. They pointed out that a national network was broadcasting the games. They marveled at the pitchers and wondered if they could hit a softball. Dominguez called the games exciting and faster than baseball.

“They’re so good!” Gomez said. Dominguez, who had never seen women’s softball, added, “I’ve learned that women are very capable. I never imagined in my life seeing women doing this, throwing this hard and playing like this.”

Once the Texas-U.C.L.A. game ended, Dominguez and Gomez followed Balkovec so she could say hello to the U.C.L.A. coaches she knew.

Balkovec introduced her players to Kelly Inouye-Perez, U.C.L.A.’s head softball coach. Gomez wanted a photo with the U.C.L.A. team, and Dominguez, while initially shy, soon relented. Inouye-Perez told her squad about Balkovec’s new gig.

“The cool part is that she’s in a power position, and it says a lot about opportunities for us as females and being a female leader and at the Yankees,” she said. “How about that?”

Off to the side, Inouye-Perez explained that her team had been fans of Balkovec for some time. And when Balkovec was promoted, Lisa Fernandez, an assistant U.C.L.A. coach and three-time Olympic gold medal winner, sent her a text message, forgetting that Balkovec had her number.

“‘Hey, Rachel. This is Lisa Fernandez, the coach from U.C.L.A., and I’m so excited for you,’” Balkovec recalled. “And I was like, ‘Lisa, you don’t have to explain to me who you are! I had your bat when I was a kid.’”

Inouye-Perez asked for a photo with Gomez and Dominguez “so when you go big league, you’ll remember who I am.” As they posed, Inouye-Perez called over to Balkovec, “Get in here, Coach.”

“Manager,” Gomez retorted with a smile.

During the drive back to Tampa, Balkovec had a few parting thoughts for her players.

First, she told Dominguez and Gomez about a pet peeve she hoped not to see during the upcoming Tarpons’ season: players lost in their cellphones in the clubhouse rather than interacting with each other.

Second, she wanted to plant a seed. Part of why she aspired to become a general manager one day, she told them, was because she wanted to overhaul the talent pipeline from Latin America. While M.L.B. teams had education programs, she felt not enough emphasis was put on developing players as humans. She noted how corrupt the international amateur signing system could be. She asked for their opinions.

Balkovec then told them about her dream that both of them would go to college. Gomez called it his Plan B.

“If you’re just a good baseball player, and you make a lot of money, that’s it,” she said, adding later, “You have to do more. Go to school. Be different. And different in this business is putting value on other things beyond money, ladies, going out — that is so common.”

“That’s the easy life,” Gomez said. But then he offered his perspective. He told Balkovec about how she grew up with more opportunities in the United States than he did in Venezuela. He explained how, when he was 12, his father asked him if he wanted to focus on school or baseball, and he chose the latter. He continued, “It’s different. We weren’t born here.”

“I know what you’re saying, but now you’re here,” she responded. “You have money and a little bit of security, so you can start thinking about other things beyond just this.” She added later, “I know you’re young. It’s OK. It’s something you need to think about in your life. What are you doing here? Just to play baseball? What’s your purpose in this world?”

“I don’t know,” Gomez said. “Baseball is still hard.”

The conversation carried on as Balkovec turned into the parking lot of their hotel. When she stopped, Gomez and Dominguez said goodbye and added something few baseball managers are likely to hear from their players.

“Rachel, love you,” Gomez said. “Thank you.”

“Thank you,” Dominguez added. “I love you.”