In the weeks before the Women’s World Cup, Sophia Smith admitted that she wanted to be the first United States player to score a goal in the tournament. Of course she did. Like every great athlete, she has long envisioned herself as a star.

Growing up in Colorado as the youngest of three girls, Smith spent years trying to keep up with her sporty sisters. She was the sibling relegated to the middle seat of the car, the one who tagged along at basketball practices, the baby yearning to be noticed.

Yet even as a young teenager, Smith said, she knew she was destined for something bigger. She told her parents that she had the talent and drive to be a “special” soccer player. Maybe the best ever. It hardly seemed like a long shot: She was not prepared, after all, to settle for anything less.

“I’m a winner,” Smith said in an interview before the World Cup. “I have to win. It makes me sick to lose anything. Card game, anything. When it comes to soccer, I just find a way.”

On Saturday in the United States’ 3-0 victory over Vietnam, Smith showed — yet again — that there was something to her gut feeling that she would be great.

In her first World Cup game, Smith scored the U.S. team’s first goal of the tournament. Then she scored its second. Later, she had the assist on its third. And even then, she thought her day could have been better.

“We could have scored several more goals,” Smith said. “Myself included.”

It was a remarkable debut, which reinforced the view of many that Smith, 22, could leave Australia and New Zealand as the tournament’s breakout star. In a team filled with promise — eight United States players made their first World Cup appearances against Vietnam — Smith once again hovered high above the rest. Not that her teammates didn’t try to keep up.

At times, it seemed as if every player on the U.S. team could have scored a goal or two, or three. Savannah DeMelo, making her first World Cup start and only her second appearance for the national team, had two great early chances. Rose Lavelle — finally back on the field after a long injury layoff — had at least two more after entering as a second-half substitute, including one shot that looked bound for success until it ricocheted off the crossbar.

Not even Alex Morgan, the star forward in her fourth World Cup, could match Smith. Morgan missed a penalty kick in first-half injury time when her low shot was stopped by the Vietnam goalkeeper, Thi Kim Tranh Tran.

“You know, we can always put more away,” said Morgan, who added that she was happy with the victory but not with her penalty attempt. “But I think the way the first World Cup game goes is not the way the last one is going to go.”

United States Coach Vlakto Andonovski acknowledged that his team — which is trying to win an unprecedented third consecutive World Cup title — should have converted more of the two dozen-plus chances they created, and said he would have liked to see more efficiency in those critical moments in front of the goal. The U.S. team has only several days to make those adjustments before it faces a much tougher test against the Netherlands, but Andonovski said that was plenty of time for his players to study what went wrong and to get back to its usual scoring rhythm.

Thursday is the deadline. The Netherlands, a team the U.S. defeated in the 2019 World Cup final, surely won’t allow as many chances, and it surely will make the U.S. work harder on defense.

Andonovski had little doubt, though, that the United States would be ready. He said he was encouraged by how his team played against Vietnam, considering the 11 starters had never played a game together, and six of them — including Smith — had never played a World Cup match at all.

“I’m sure the nerves had something to do with it,” he said of the substandard finishing. “So I’m not worried about it.”

He added that he was encouraged by the style of soccer that the team played, and pleased with all the opportunities it created. Smith was just as upbeat. Once the team loosens up a bit and gets more touches and strings together more passes, she said, it will “settle down and feel more confident.”

She did admit, though, to feeling nervous before the game, a sensation that she said was a first for her.

That means she didn’t feel nerves when she helped Stanford win an N.C.A.A. championship in 2019, which included her scoring a hat trick in the semifinal. Or when she entered her first professional game with the Portland Thorns, in 2020, and scored after only three minutes.

The World Cup, though, is another level entirely, even against Vietnam. Smith is at a new point in her career now, with new emotions and higher stakes. But ever since she was a kid, she has been ready.

“Whoever scores, whatever the score is, a win is a win,” she said in the days before the Vietnam game. “And if it takes me scoring a lot of goals for us to win, I’ll do that.”