Poland have only featured once at the European Championship - failing to progress past the group stage in 2008 - but Szczesny believes people are finally beginning to take notice of just what they are capable of.
"I think Poland have a chance of doing well," the goalkeeper told the Official Arsenal Magazine. "The atmosphere around the national team has changed a bit and people have realised that we actually have world-class players.
"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.
"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."