The US beat Germany 1-0 in the semi-finals thanks to a dramatic 95th-minute winner from Sophia Smith on Tuesday.
That victory came a year to the day after their shocking early exit from the Women’s World Cup, where they fell in the last 16 to Sweden.
Their fall from grace – they had been world champions since 2015 – led to Hayes’ appointment and the subsequent revival in the early months of her tenure.
“It’s been noted on more than one occasion what happened at the World Cup,” said Hayes, who led Chelsea to 13 major trophies in her 11 years in charge.
“We want to create a new history. We want to create our new identity and that journey has been about getting those things right. It’s been an unbelievable journey so far to get to this point.”
After securing a spot in their record-extending sixth gold-medal match, the US hope to return to the heights of women’s football in Paris.
They saw off European finalists Germany and Asian giants Japan in the knockout stages, having gone four hours without conceding.
Forward Smith said: “It’s a challenge to build trust with a new coach, let alone a few months before a world tournament, but she just came in flying and we absolutely love her.
“She has worked every day to build our trust and show us that she genuinely cares about us, not only as players, but as people. That goes a long way.
“She’s such a great coach, such a great mentor. She knows exactly what to say and when you need to hear it. We’re a completely different team.”