Gareth Southgate's side will head to Germany as one of the tournament favourites after finishing as Euro 2020 runners-up and reaching the World Cup quarter-finals two years ago.
England have never won the European Championship and last lifted a major prize at the 1966 World Cup.
Newcastle right-back Trippier, who will captain England in Monday's friendly against Bosnia and Herzegovina, is convinced the Three Lions are primed to get their hands on silverware at last.
"I've said it many times, we shouldn't be shy to say that we can win it," the 33-year-old told reporters on Sunday.
"We're not saying that in an arrogant way. We've got a great squad, top manager, top staff. We've been so close recently over so many years it's just about taking that next step now.
"I fully believe with this squad that we've got, we can go all the way. But we need to earn the right.
"The most important thing is the togetherness we've got in the squad. It's unbelievable, probably the best I've been involved in, so we're all looking forward to it."
Trippier is captaining England for the Bosnia match in the absence of regular skipper Harry Kane.
Bayern Munich striker Kane missed the final two games of his club's season with a back injury sustained in the Champions League semi-final second-leg defeat against Real Madrid.
It will be a proud moment for Trippier when he leads England out at Newcastle's St James' Park, with his seven-year-old son Jacob at his side.
"It's going to be very special, obviously, at the stadium where I play week in, week out. I've got to thank Gareth again for giving me that trust," he said.
"But for me if I have the armband or not, if I play or not, I'm always there, I'm always ready for the team and I'm a leader with or without the armband. I've never had it on a permanent basis.
"That's the type of character I am but to lead the lads out, it's very special. My son will be mascot as well, so that's even more special, so a really proud moment for myself."