Monica Puig gazed out at her fellow Puerto Ricans jamming the parade route, and in their eyes she saw hope.

They hailed her with “a sense of satisfaction,” she recalled on Saturday, “and a sense of belief that things are going to get better”.

Throughout her stunning run to the Olympic tennis gold medal, Puig embraced the symbolism of each upset victory.

“If Puerto Rico channels that same energy and belief that things will get better and working for the better of the island, the better of the community, things will improve,” Puig said four days after the US territory honoured its Olympic team and, above all, its first gold medallist.

The world’s 34th-ranked women’s tennis player met with a roomful of reporters Saturday, exactly two weeks after she beat Australian Open champion Angelique Kerber in three sets in the final in Rio de Janeiro.

The 22-year-old realises some people deem her gold medal “a fluke”.

After all, Puig has never made it past the round of 16 at a major.

And at the US Open she’s never advanced beyond the second round.

Puig is already bracing herself for the reality that her run at Flushing Meadows could fall well short of what took place in Rio.

“I’m 22 years old. There’s still a long way for me to go, a long stretch of career,” she said.

“If anything happens, any kind of slip-up, it’s not really going to be a big deal, because I have a process and I have a long-term view of where I want to go.”

Which isn’t to say she expects a slip-up.

“I know that the Olympics wasn’t a fluke for me, because I have worked very hard to get to where I am,” Puig said.

“But that moment, nobody will be able to take away.”

After Rio, Puig spent some time with her family in Miami, where she lives. Then it was on to the island “where the big party was waiting”.

Puig faces 60th-ranked Zheng Saisai, who upset Agnieszka Radwanska at the Olympics, in the first round Monday.

She originally wasn’t seeded at Flushing Meadows, which meant she could have faced a top player in her opening match, but she moved up to the final seed when Sloane Stephens withdrew because of an injury.

It’s the first time Puig has been seeded at a major, and in what was a breakthrough season even before her golden moment, she’s starting to grow comfortable with those sorts of roles.

“I feel like I finally understand what I’m doing when it comes to tennis,” she said.