Wales secured a 1-0 win over Ukraine in their qualification playoff final on Sunday and will now play in Group B along with the U.S., Iran and neighbours England in the tournament which starts on Nov. 21.
"We have played against the USA. We know they are a really strong outfit. We played against their European-based players, in my first game," Page told BBC Wales, referring to a 0-0 friendly in November 2020.
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"They [and Iran] are winnable games and when you play against a home nations team, anything can happen," he added.
"We will go out there with the confidence we have had going into any game. We will go toe to toe with anybody -- bring it on. That's the attitude we have got in that changing room."
Although the last time Wales featured in the World Cup finals was in 1958, the existing squad have gained big-tournament experience through the last two European Championship campaigns.
U.S. manager Gregg Berhalter, meanwhile, said it's "full steam ahead" for his side's World Cup preparations now that Wales has been confirmed as the final Group B addition.
"It's a great feeling," Berhalter said following the U.S. team's 0-0 draw with Uruguay on Sunday. "It's kind of strange when you get drawn into a group and it's one of three teams that you can play. So in terms of prep, it gets stalled a little bit, but now it's full steam ahead into concentrating on Wales."
Berhalter added that his "heart goes out to Ukraine" given the ongoing invasion that the country has suffered at the hands of Russia.
"The whole world was probably behind Ukraine and wanting them to go to the World Cup," he said.
U.S. and Chelsea midfielder Christian Pulisic, added that he didn't think there would be any advantage to being familiar with the Welsh players, several of whom play for clubs in the English Premier League.
"I think we know what their team is about and we're gonna have to put in a good performance if you want to win," he said.
Wales is ranked 18th in FIFA's rankings, three spots behind the U.S., which hints strongly at an evenly matched contest, where either side will like their chances of winning.
"It's a great group and we're excited to play those teams," U.S. defender Walker Zimmerman said. "They each have their different challenges and to get to play a guy like Gareth Bale, I think it's something we can all be excited about."
Page believes that those campaigns have helped the nation's fan base to unite behind the team in a country where rugby union has long been viewed as the national sport.
"Growing up in the valleys it was all about rugby. We had Cardiff City and Swansea City in the old fourth division and rugby was probably the No. 1 sport. The tides have turned slightly now," he said.
"It is because of what the boys are doing and success drives that. When you are winning it helps for people to take notice. Football has probably overtaken rugby at the moment as the number one sport in Wales," added Page, who has been in charge of the team since Ryan Giggs stood down from the position while facing allegations of assault.
Page also gave credit to former manager Gary Speed for laying the foundations for the upturn in fortunes for the national side before his death in 2011.
"Gary Speed started it 12-13 years ago and I want to dedicate this win and qualification to him and his family," he said. "There was a change in the tides and we created a culture and identity of how we wanted to play and it started then."
ESPN's Jeff Carlisle also contributed to this report.