By simply stepping onto the TD Garden ice, the Notre Dame Academy girls’ hockey team will make history.

The program was launched in 2003. Sunday, the Cougars (17-4-2) will skate in the Division 2 final for the first time.

Their head coach has taken more than a few skates around the Garden ice. A member of the silver medal-winning Team Canada at the 1994 Olympics, Jean-Yves Roy saw action in 54 games on the wing for the Bruins from 1996-98.

“I’ve spent a few days there myself,’’ the 47-year-old Roy said with a smile after his squad punched its ticket with a 9-3 win over Matignon in the state semifinals Monday in Bourne.

“But not as a coach with NDA. This is our first time at the Garden.’’

The state final is the culmination of a significant three-year turnaround for the Cougars. NDA won just two games during the 2012-13 season, the year before Roy was hired.

Fast forward three seasons, and the Cougars are back-to-back Catholic Central champions. Wellesley stands in their path.

“I had the seniors stand up in the locker room and asked if they ever thought this would be possible three years ago,’’ Roy said after the victory over Matignon at Gallo Arena.

“Not a chance. We came a long way, and hopefully it pays off.’’

Roy’s lengthy playing career began at the University of Maine, where he racked up 203 points in three seasons, earning all-Hockey East and All-American honors. At the professional level, he skated in the American Hockey League, the NHL, as well as leagues in Austria, Germany and Switzerland.

After his playing career ended, he worked as on-ice official in the ECAC and Hockey East.

When Notre Dame athletic director Donna Brickley was seeking a coach for the girls’ program, she called Roy, a Marshfield resident.

“It was probably over the course of a couple years that I started hearing his name,’’ Brickley said. “We’ve been thrilled to have him since. He’s been very selfless with his time and very helpful with the kids.’’

In his first season behind the bench, NDA finished 5-10-5 with a schedule that was loaded with Division 1 foes.

Last year, the Cougars jumped to 14-5-3, earned the 11th seed in the Division 2 tournament, and beat Springfield Cathedral in the preliminary round of the tournament.

“They had had such a bad experience the prior season, I think they were starving for guidance and leadership,’’ Roy said. “I implemented a system and the girls bought into a system and believed in it.’’

His system is simple: don’t put yourself above the team; no selfish play on the ice, no poor decisions off it.

As a freshman at Notre Dame, Lizzy Bell rode the bench on a team that won two games. Now, the Quincy resident is the starting goalie for a squad one win away from a state title.

She credited Roy for his ability to craft near-perfect game plans. It’s just a matter of execution.

“A lot of people have so much talent but can’t communicate to people who are learning,’’ Bell said. “It’s really cool to see how it works.’’

Last winter, Roy enlisted the help of Rachel Llanes , a former standout at Northeastern University. A player with the Boston Pride, which won the NWHL in the league’s inaugural season, she also works as a strength and conditioning coach.

Llanes ran skill sessions on the ice last season, and encouraged Roy to explore off-ice, strength-building workouts.

“Right when I met him, he wanted to make a difference at NDA,’’ Llanes said. “I told him to get an edge, we needed the off-ice work to help the girls and he was all for it.’’

Under the direction of Llanes, the Cougars trained at DB Performance in Hingham once or twice a week during the season. The NDA players cycled through speed and agility workouts, weight training and recovery exercises.

“I thought it would be a good role model with the girls to have another high level female athlete to show them different things,’’ Roy said.

Although Llanes has taken a step back this season, the off-ice work continues to make a difference, especially with team chemistry.

“When you’re off the ice, you create a little more of a bond, especially when the coach isn’t there,’’ Llanes said.

Roy has seen the impact on his own daughter, Gabby, an eighth grader who leads the Cougars with 33 points, including both goals in a 2-1 win over Winchester in the first round of the tournament.

“If she hadn’t gone through all the training and strength building, I don’t know if she would’ve scored,’’ Roy said.

Roy rolls out three and four lines consistently, relying on his players’ execution and conditioning to wear teams down. The Cougars scored 30 goals in tourney wins over Mansfield/OA/Foxborough (11-3), Winchester (2-1), Methuen/Tewksbury (8-2), and Matignon (9-3).

Gabby Roy said her father is able to separate coaching from parenting, describing him as a serious coach who focuses on efficiency and details.

“He doesn’t usually like to yell,’’ Gabby said. “He likes to have a high-tempo practice. There’s not a lot of standing around.’’

But for all of Roy’s attention to detail, there have been plenty of lighter moments. Bell recalls the coach singing songs at the front of the bus to away games, using a hockey stick as a pretend microphone.

“It’s funny because he’s this serious coach on the outside,’’ Bell said.

Roy seems to have found the right combination of focus and freedom.

Senior forward Caroline Hocking (21 points), like Bell, has played on teams that have struggled. Now, she’ll have a chance to end her career in the best possible way.

“We’ve really come together as a team,’’ said Hocking. “Everybody works hard, works together, and it’s something we’ve all waited for for four years.’’

Matt MacCormack can be reached at matt.maccormack@globe.com.