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HARRISON, N.J. -- United States women's national team head coach Emma Hayes said her team still needs to improve its decision-making in the final third, but she saw signs of progress in the 1-0 win over Mexico at Red Bull Arena on Saturday.

Hayes' third game in charge of the U.S. was the Americans' penultimate match before the Olympics and its first with the roster that leaves for France next week in search of the program's first Olympic gold medal since 2012.

"If we use [the Concacaf Gold Cup] as a reference point, I think it's fair to say this game was much more measured, much more controlled," Hayes told reporters. "[We] limited them to very little, so [it's] a step in the right direction."

The victory comes less than five months after Mexico's historic 2-0 victory over the USWNT in the group stage of the Concacaf W Gold Cup, the Americans' first loss to Mexico on home soil.

Saturday was a more measured game that saw the USWNT retain 70% of the possession and keep Mexico from finding the counterattacking opportunities that allowed the visitors to thrive at the Gold Cup.

USWNT forward Sophia Smith broke the deadlock in the 64th minute. Rose Lavelle played a ball behind Mexico's defense and sprung Trinity Rodman free down the USWNT's right side before Rodman found Mallory Swanson at the top of the box.

Swanson opened up to continue switching the ball to Smith, who squared up her defender and buried a shot with her right foot.

Until the goal, the USWNT was largely in control of the match but wasteful in front of the net. The USWNT ended the game with 17 shots and 1.94 expected goals -- while limiting Mexico to .07 xG -- per TruMedia. Smith admitted it was frustrating up until her tally, but said she isn't concerned.

"I mean, we're not worried about it," Smith said. "I know Trin can score goals, I know Mal can score goals, I know I can score goals. That stuff is -- it'll come. We just need to be patient with ourselves"

The Americans' best chance of the first half came in the 21st minute on a sequence that eventually ended with Rodman hitting a shot that just missed the far corner. Rodman was a catalyst in the buildup of the play, dropping deep to receive the ball from Naomi Girma and then turning to get involved in the play further up the field. Rose Lavelle played Rodman toward the endline, and Smith eventually got on the end of a shot that was saved by Mexico goalkeeper Esthefanny Barreras.

Hayes said "small details" are the difference between Saturday's 1-0 result and a larger margin of victory. She pointed to minor details such as checking to see the goalkeeper's position before shooting.

"You only have to see from just an xG perspective at the end of the game: It's two-point-something and should be much bigger because for the chances we've created, we're not hitting the frame enough," Hayes said. "I still think that's something to add, but I think the difference in momentum from first half to second half was even bigger for us. Much more controlled."

Captain Lindsey Horan moved higher up in the midfield in the second half after playing next to Sam Coffey in a double pivot in the first half, and the USWNT found success immediately. Two minutes into the second half, Swanson put a shot just wide of frame on a feed from Smith. Five minutes later, Smith got on the receiving end of a direct ball over the top from Horan.

Smith soon found the back of the net, then hit the post nine minutes after her goal.

The victory was the third in as many games for the USWNT under Hayes, who finished out the European season with Chelsea before joining the team.

Hayes & Co. have less than two weeks to be ready for the Olympics, where they hope to avoid being the first team in program history to fail to win either a World Cup or an Olympics in a cycle of major tournaments. The USWNT was eliminated from last year's World Cup in the round of 16, in a penalty shootout against Sweden.

The Americans have already had to adapt: On Friday, Hayes and U.S. Soccer announced that midfielder Catarina Macario, who was originally on the 18-player Olympic roster, had been replaced by forward Lynn Williams. Macario is dealing with "knee irritation" following her recent return from a torn ACL suffered in 2022.

The USWNT has plenty of attacking talent beyond Macario, and the starting lineup that Hayes rolled out on Saturday is likely the team she will entrust at the Olympics. Progress was on display, but there was clearly room for improvement.

"I think we're only scratching the surface," Hayes said. "I think there's a lot of layers to go from everyone."