As a 10-year-old in Westport, Conn., Gwen Goldman sat down in her parents’ home with one goal in mind. She wanted to be the Yankees’ batgirl.

So in 1961, she penned a letter to the Yankees’ general manager, Roy Hamey, asking him to let her do her dream job. Goldman vividly remembers the day she got a response — she pulled the letter out of the mailbox and was ecstatic to see the Yankees’ logo on an envelope with her name on it.

But Hamey wasn’t willing to let her dream come true. He wrote back to her in June 1961, “in a game dominated by men a young lady such as yourself would feel out of place in a dugout.”

“I am sure you can understand,” he added.

Goldman kept the letter on her bulletin board as a child. It now resides in her house, framed on the living room wall.

“Of course you’re disappointed; that’s something you really hope for and you really want,” Goldman said in a phone interview. “But I kept that letter, number one, because it was the Yankees, my love, the team … and you never know. It’s a hope.

“Did I ever think? I hoped, but I never imagined that this was going to happen at this stage in my life.”

After her daughter Abby forwarded an email and a photo of the letter to the team, it found its way to the inbox of GM Brian Cashman. And last week, on the 60th anniversary of Hamey’s note, Cashman surprised Goldman on a Zoom call with her family to deliver a different message: She would finally be able to live out her dream.

“Here at the Yankees, we have championed to break down gender barriers in our industry. It is an ongoing commitment rooted in the belief that a woman belongs everywhere a man does, including the dugout,” Cashman read to Goldman. “Despite the fact that six decades have passed since you first aspired to hold down the position as a New York Yankees batgirl, it is not too late to reward and recognize the ambition you showed in writing that letter to us as a 10-year-old girl.”

So Monday night, Goldman was the honorary batgirl during the Yankees’ 5-3 loss to the Los Angeles Angels, part of the team’s HOPE Week initiative, a program started in 2009 that aims to promote acts of goodwill that provide hope and encouragement to others.

Goldman’s day was packed from the moment she got to the stadium. She had a locker with her name on it and took the field in full uniform. She also threw out the first pitch, stood with the team for the national anthem and posed with the umpires when the teams brought out their lineup cards.

“It was a thrill of a lifetime — times a million,” Goldman said during a fourth-inning news conference. “And I actually got to be out in the dugout, too. I threw out a ball. I met the players. Yeah, it goes on and on. They had set up a day for me; that is something that I never would have expected.”

Goldman, who spent 31 years as a social worker in the Westport school system, had no idea the video call would end with that invitation. She has two grandchildren who just finished preschool and first grade, so she believed she was getting on a call to celebrate the end of their school years.

When Goldman and her husband, Pete McLoughlin, hopped on the call, she saw a few extra people she didn’t recognize. She assumed they were work colleagues of her daughter. Instead, they were members of the Yankees’ organization. Senior vice president and assistant general manager Jean Afterman, general partner Jennifer Steinbrenner Swindal and Yankees ace Gerrit Cole were also on the call.

“Next time you go on a Zoom call, never assume what’s going to happen,” Goldman said.

Goldman said she was dumbfounded and speechless at first and then overwhelmed with excitement.

She remembers the first time she walked into Yankee Stadium as an 8-year-old. Her dad’s employer had box seats along the first base line, and Goldman brought her glove in case a ball came her way. She remembers seeing the batboys on the field and telling her dad, “ ‘I want to do that. I can do that. I know how to pick up the bat and throw a ball.’ I remember saying I wanted to be a batboy.”

On Monday, Goldman drove with her husband from their home in Connecticut to the stadium. She joked that morning that she was checking and rechecking maps of their route to make sure they wouldn’t be late. The rest of her family — her two daughters, son-in-law and two grandchildren — was also there.

She has been to the old and the new Yankee Stadium many times since, and her feelings when she’s there have not changed.

“It does it to me every time,” Goldman said. “It was so magical: the smells and the sights and the sounds. Hearing that ball be hit, that crack, just unbelievable. It was bigger than life, and there I was with my dad doing this.”

She thanked her daughter for starting the process and the Yankees for “being at the forefront of believing about breaking down those gender barriers.

“The letter Brian Cashman wrote to me, it’s just beautiful and speaks a lot to who they are as an organization, trying to do what’s right,” she said. “… I picked the right team to be a fan of, didn’t I?”