GANGNEUNG, South Korea — The sound of redemption was a thud, one that echoed through an arena 7,000 miles from home — the sound of a puck hitting the left shin pad of a 20-year-old goaltender who was seven months old the last time the U.S. women’s hockey team won gold.

The realization of redemption came a millisecond later when that goaltender, unflappable Maddie Rooney, scooped the puck off the ice and tossed it away. It was as if she tossed two decades of disappointment and demons and silver-covered memories away with it. As soon as she did, this generation of American women’s hockey players standing on the bench raised their arms, the weight finally lifted off their shoulders.

When Rooney stopped Canada’s Meghan Agosta — the sixth shooter in what was supposed to be a five-person shootout — she sealed a 3-2 victory for the Americans, and their first Olympic gold medal since 1998.

If these teams played a seven-game series, a safe bet would be a shootout in the seventh. If they played 101 times, they would need overtime in the 101st.

That four years funnel to this, to one puck and one save, sometimes feels unfair. But if the Americans had had annual chances to beat back the Canadians for this Olympic medal, none of what happened over those three riveting hours — in front of a crowd so alive it could barely breathe, with players so invested their lives literally changed — could mean so much.

“It’s definitely part of our legacy,” Hilary Knight said. “I don’t know — the things that we’ve gone through as a team, on and off the ice, the characters that we have in the room, it’s incredible.”

When exorcisms can come only every four years, demons have time to reproduce, and demons leave scars. This team’s previous Olympic showing was a collapse in Sochi that sent it spinning. So no one needed clarification when captain Meghan Duggan opened these Games by saying, “This is the team.” This is the team that could heal the wounds. This is the team that could make it all worthwhile. This, of course, is the fourth straight team to think of itself that way.

Members of the U.S. Women's hockey team want to inspire on and off the ice. After winning a battle for equal pay, they are now aiming for gold at the 2018 Olympics. (Alice Li, Ashleigh Joplin, Zoeann Murphy/The Washington Post)

Even before taking the ice Thursday, the U.S. women waded through trouble. This team shared the risk of boycotting the world championships, hoping to be rewarded with equal pay, and won. It waited out Hurricane Irma together in a hotel lobby, and survived. It remained steady through the departure of one coaching staff, then the relatively late arrival of another, and expectations didn’t change.

Then came the pressure of the Olympics, which had become that most dreaded of sports evils: “a thing.” The Americans had beaten the Canadians for gold in the past four world championships, and seven of the past eight. Normally, that counts for something. In this rivalry, it only served as evidence that the Americans had trouble when it mattered most, some weakness in the biggest moments.

But this time, the United States scored first, a puck tipped in by Knight in the first period. The Canadians grabbed two goals in five minutes in the second period — the kind of abrupt twist of fate that always defined these games.

This time, the Americans trailed into the third, then into the final 10 minutes. With less than seven minutes to go, the Canadians made a mistake: A puck slipped away as both teams changed lines. Two-time silver medalist Monique Lamoureux-Morando picked it up and took it to the goal. She buried it. The Americans lived, then lived on through 20 minutes of four-on-four overtime, including a Canadian power play in the closing seconds. The game headed to a shootout, something veterans on both sides regretted afterward. It just didn’t seem right.

“But you have to decide the game somehow,” said three-time Olympian Kacey Bellamy, as if acknowledging that these titans could have played to eternal deadlock.

After five shots each, the deadlock remained. Jocelyne Lamoureux-Davidson — the tie-forging goal scorer’s twin sister — was the sixth American to try. She deked up, then left, then pulled the puck back right, where Canadian goalie Shannon Szabados had no chance.

“This is a very classic example of how hard it should be,” U.S. Coach Robb Stauber said. “Winning a gold medal should be very difficult.”

So much goes into each little moment, and so many moments go into a gold. Like so many of her teammates, Lamoureux-Davidson rededicated herself after Sochi, made the team journey her own, and began training with her old University of North Dakota coach, Peter Elander. He taught her that move — called the “Oops! . . . I Did It Again,” after the Britney Spears song — an apt title given Lamoureux-Davidson said she “butchered it thousands of times while practicing around tires” in the offseason.

The Americans came within five minutes of gold in 2014. Because of those five minutes, Lamoureux-Davidson spent four years doing a little bit more, operating on the assumption that one puck would change everything.

One puck did change everything — though after all that, Lamoureux-Davidson said she hardly remembers the shot. Next thing she knew, Rooney stopped Agosta, and “Born in the U.S.A.” was playing as the 28-year-old Lamoureux-Davidson retrieved an American flag she had folded away for seven months. The benefit of a once-every-four-year schedule is it does allow for planning.

“We’ve played this game in our minds a million times,” Duggan said. “And we’ve won it every time.”

“I remember jumping on my couch, cheering on Cammi Granato and Team USA, Angela Ruggiero,” Knight said. “To be able to be here 20 years later, getting the gold medal, it’s pretty incredible.”

Ruggiero, now with the International Olympic Committee, happened to be the one who handed them medals Thursday. She was on that 1998 gold medal team, then the subsequent teams that settled for two silvers and an embarrassing 2006 bronze.

She — like so many others over the past two decades — dedicated years of her life to bringing the gold medal back home. She, like all the others, heard hopes become reality when that puck hit the pad of that precocious young goaltender, sealing redemption for this U.S. women’s hockey generation, and undoubtedly inspiring the next.

Ice hockey, in under 60 seconds. (Victoria Walker, Osman Malik/The Washington Post)

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