Albania have already achieved their dream by simply qualifying for their first major tournament and they hope that the lack of psychological pressure in France might even take them beyond the group stage.
Seemingly the eternal also-rans, Albania had never previously reached the World Cup or European Championship and the 3-0 win over Armenia that clinched their place in Euro 2016 sparked wild scenes at home and among thousands of Albanians abroad.
"Getting to the finals means we have already won our European Championship. We managed to qualify directly," said national soccer federation spokesman Tritan Kokona.
"We have a weapon we intend to use: we carry no psychological burdens," Kokona told Reuters.
Albania will play hosts France, Romania and Switzerland in Group A and, outgunned by rivals with more experience and international stars, no-one is setting their sights absurdly high.
All the same, Italian coach Gianni De Biasi and soccer federation chief Armando Duka harbour hopes of making it through the group stage.
"We shall go to France to play football, not as tourists, but we are not making plans. Our group is difficult, but we have proved we can beat anyone." said Duka.
The Albanian diaspora in Europe, home to most of the team's players from Kosovo and Macedonia, have already bought 26,000 tickets for the group matches.
However, it will be understandable in Albania's first match against Switzerland if some supporters feel a clash of loyalties.
Almost half of Switzerland's main line-up are of ethnic Albanian origin from Kosovo and Granit Xhaka, a pillar of the Swiss team, is likely to be playing against his own brother Taulant.
In his four years as coach, De Biasi has tried various players to find the perfect combination but though Albania play a strong defensive game their attack lacks punch.
Striker Bekim Balaj sealed victory over Portugal in their opening group match with a powerful shot from an Odise Roshi cross that wrong-footed an experienced Portuguese defence.
It was defenders Mergim Mavraj and Berat Xhimshiti, Shkelzen Gashi and Armando Sadiku in mid-field who helped Albania to qualify with goals against Armenia at home and away.
With those limitations in mind, Astrit Hafizi, who coached the national side from 1996 to 1999, offered a more realistic appraisal of prospects.
"If our opponents and our team were at the top of their game, our weaknesses would be revealed," Hafizi told Reuters.
"We tend to be very dangerous for those who underestimate us. However, our rivals will see us as the underdog they will try to beat so they can allow themselves a draw with the others," he said.