As one of the host nations Poland qualified automatically for the competition but they’ll face a stern test in Group A against Russia, Czech Republic and Greece.
The Arsenal keeper believes there is a confident mood in the squad ahead of the tournament and hopes the team can live up to their own expectations.
He told club's official website: "It's all there for us to go and have a successful tournament - I think it’s the strongest Poland team the fans have seen for years so hopefully we won’t let them down.
"I think Poland have a chance of doing well. The atmosphere around the national team has changed a bit and people have realised that we actually have world-class players."
Szczesny has singled out Borussia Dortmund trio Jakub Blaszczykowski, Lukasz Piszczek and Robert Lewandowski as three key players for the Poles ahead of the tournament.
The 22-year-old believes their quality and experience will be vital, after their success helping Dortmund to the Bundesliga title this season.
He added: "The three players from Borussia Dortmund are as good in their positions as anyone in Europe – Lukasz Piszczek is a right back and I’d easily put him in the top three in Europe, his fitness levels are something I've never seen before."Jakub Blaszczykowski, the skipper, always steps up for the national team while Robert Lewandowski is just a natural goalscorer. We've got plenty of others who can make an impact too - Ludovic Obraniak in midfield is a fantastic player and we have some solid defenders."