Sophia Smith, who scored the only goal in a 1-0 semifinal win over Germany, has scored three goals in the Olympics for the United States, which faces Brazil for the gold medal on Saturday. Aurelien Morissard/Associated Press

PARIS — Just when it appeared the U.S. had conceded its dominance with an early exit from Women’s World Cup, the Americans have roared back under new coach Emma Hayes with an undefeated run in the Paris Olympics.

There’s one more hurdle: The U.S. faces Brazil for the gold medal on Saturday at Parc des Princes.

“We had a tough year last year in every way possible,” forward Sophia Smith said. “But I feel like this is a new year and we’re really just showing the world that we never did drop off. We just needed a learning year and a growth year. We’re back, and hopefully on top after this next game.”

The United States is the winningest team at the Olympics with four gold medals, a silver and a bronze. But the U.S. hasn’t won a gold since 2012 in London. The team was knocked in the quarterfinals of the Rio de Janeiro Games and settled for bronze three years ago at Tokyo.

Last summer as defending champions, they were eliminated from the World Cup earlier in the tournament than ever before. Since then, the Americans dropped to No. 5 in the FIFA rankings, the team’s lowest rank ever.

“I’ve always said I want our players to look at our history as a privilege and something that can help guided us,” Hayes said. “But ultimately, I want us to forge our own path and I want to forge a path based on the values and the ambitions of this current group.”

Hayes, who arrived in May after wrapping up the season with Chelsea, has given the team new life.

So far the U.S. hasn’t lost at the Olympics, with 11 goals scored while conceding just two. The forward trio of Smith, Trinity Rodman and Mallory Swanson have three goals apiece.

The team is playing with renewed joy and a determination to re-establish American dominance. The players got a visit before the tournament from the entire squad that won the 1999 World Cup, the so-called ’99ers that included Brandi Chastain and Mia Hamm. And then there’s the intra-squad karaoke battles in their downtime in France.

Captain Lindsey Horan said the key has been to live in the moment.

“That’s been the most enjoyable thing, because you’re just staying present. You get to enjoy it with your team and see smiling faces all over the place,” the 30-year-old midfielder said. “And the karaoke machine is coming out going into the gold medal match, it’s amazing.”

The United States advanced to the final in France with an 1-0 extra-time victory over Germany in Lyon. Smith scored the lone goal.

The Brazilians upset World Cup champion Spain 4-2 in the other semifinal Tuesday in Marseille.

Brazil gets its captain Marta back after a two-game suspension that kept her out of the quarterfinals and semis – the result of a straight red in the final group-stage match.

The Americans previously faced Brazil in gold medal matches at the 2004 and 2008 Games, coming away with the title in both tournaments. The two silvers are the only medals Brazil has won.

“They’re building something special, like us, too,” Brazilian midfielder Angelina said about the Americans. “We are also building something new. I know it’s going to be a very tough game, so we are just preparing for that.”

Rodman said she’s personally grown, along with the rest of the team, since the World Cup disappointment.

“I feel like this time around it’s just more fun because we’re working so hard and we’re meshing and we’re doing so much behind the scenes,” Rodman said. “I just feel like we’re all free, which has been so nice to see. And I feel like we’re just like building on that. So that’s been great this tournament so far.”