The trophy has already been to the 31 other participating nations ahead of the quadrennial tournament, which starts in Australia and New Zealand on July 20.
With Hunt looking on, Briana Scurry, a World Cup winner with the United States in 1999, and New South Wales Premier Chris Minns unveiled the trophy at Taronga Zoo beside Sydney's harbour.
"It's really, really surreal to be here in front of the trophy and to have it here in Australia," Hunt said as she is hoping to be in the Matildas squad for the tournament.
"I'm honestly so excited and that's something I want our team to strive for, and have the belief that we can do it. So I think that once we have that, it's not out of reach.
"So I look at it and think that this is something bigger for Australian football."
Only former winners and heads of state are permitted to touch the trophy, which will be presented to the winning captain at Sydney's Stadium Australia after the final on August 20.