Sondergaard's 13th-ranked squad face the European champions in a Group D match at the Women's World Cup, with both teams on three points after identical 1-0 victories.
"We hope we can spring a surprise," he said.
"There's a World Cup every four years, you don't get many of these opportunities in your career. It would be a mortal sin not to enjoy it."
There is a familiarity between the two teams, Sondergaard said, with several of his players playing on Women's Super League sides alongside or against Lioness players.
Asked if that makes fourth-ranked England an easier opponent for his 13th-ranked team, the coach said: "It's easier. But that said, it's not going to be easy."
Bayern Munich midfielder Pernille Harder, who is key to Denmark's play, knows some of the England players better than most, particularly Millie Bright, her former team-mate at Chelsea.
"I have felt Millie in training," Harder said with a laugh.
"She's going 110% into the duels. She's a great player. Obviously, yeah, she's tough. It will be difficult, but I will do everything I can do to also make it difficult for her."
The 30-year-old Harder said familiarity is not necessarily an advantage for either team.
"Both teams know much about each other. But of course, I think it's always nice to know who you're going up against," she said.
"I think the fact that some of the players on our team are playing in England ... it means that you know what you're going to expect from them. You have done it before.
"That can be some kind of security in a way, compared to when we played against China when we had no idea about the players."
Denmark's opening game against China was in Perth, a five-hour coast-to-coast flight from Sydney. England, meanwhile, opened their campaign against Haiti in Brisbane, a short one-hour flight away.
"I think we saw (the long travel) as a problem before we came to Australia but now we have gotten used to it... and I think we travel very comfortably," Sondergaard said.
"And at least in training in the morning, they looked very fine."
Denmark face Haiti in their final game of the group stage on Tuesday.
