The eyes of Europe will fall upon Paris, Solna, Zagreb and Bucharest on Tuesday evening. It is in the Algarve, however, where a significant piece of history will be made.

Gibraltar, the Rock that fewer than 30,000 people call home, will play their first full international fixture against Slovakia. It follows a bitter 14-year campaign for the right to Uefa eligibly, fought in the face of Spanish opposition, which eventually ended with victory for the British territory in May.

The Estádio Algarve in Portugal, Gibraltar's home in the short term, could hold the country's entire population. Allen Bula's side – comprised of policeman, firemen and civil servants – have made the four-hour trip across Iberia because their own Victoria Stadium is not big enough to fulfil Uefa's international criteria. It is the only pitch available for Gibraltar to train on, other than one that belongs to the UK Ministry of Defence.

It is a tale one would normally expect to hear in the early rounds of the FA Cup, only on a grander scale. The majority of Gibraltar's players have day jobs but on Tuesday night they will be lining up against a squad that includes stars from Liverpool, Olympiakos and Napoli.

Bula called up the former Manchester United defender Danny Higginbotham, his nephew, via Twitter – meanwhile, the striker Jeremy Lopez has revealed certain employers do not accept letters of exemption from work issued by the Gibraltar Football Association. Uefa's 54th member state is an eclectic mix of individuals plucked out of a playing pool of approximately 1,400.

These are the challenges that currently face Gibraltar. Bula has ambitious aims and is confident his side will not become European whipping boys alongside the likes of San Marino. Between 500 and 1,000 fans are expected to travel to the game and the Gibraltar FA chief executive, Dennis Beiso, admitted it is a step into the unknown.

"This means everything, it's difficult to put into words," Beiso said. "It's the result of a long, long struggle but we feel we deserve to be here. Our association was established in 1895, which makes us the seventh oldest national association in Europe. Football is a daily passion for Gibraltarians – a lot of people live for football in Gibraltar. As much as 10% of the population are involved in the game.

"We're very excited, it's obviously a very historic day for us. We've been working very hard for almost two decades now and a lot of people have put in a lot of hard work just to make this day a reality. We're very much stepping into the unknown, we know that Slovakia will have an extremely high level compared to us. For our boys, with a few exceptions, this will be a completely new experience. Nerves will play a part but I'm sure the players are going to give a good account of themselves.

"They are committed lads. Because of what this game represents I am sure they will give 100% on the pitch and maybe we will be able to spring a surprise."

Spain, which claims ownership of the territory on its northern tip, fought Gibraltar's effort to become official Uefa members as it feared similar Catalan or Basque teams could emerge in the future. Uefa has ruled that Spain and Gibraltar cannot be drawn in the same group during qualifying for the 2016 European Championship, a tournament that Bula has in his sights.

On the game against Slovakia, the manager said: "We are looking at the nerves of our players. It's something new, the historic moment, the emotion. One minute [into the match] and it's got to be out of the way. If not, that can play against us but we are going out to win."

Bula believes his side are capable of matching Malta, Liechtenstein and Andorra in the early stages of their development. Gibraltar beat the Faroe Islands 3-0 in a friendly in 2001 but establishing themselves as a recognised and dangerous nation to play is a challenge that will take some time. Beiso added: "There were times when we doubted it would ever happen. We were up against significant forces, both in the footballing and political sense, but we were confident our position was right on moral and sporting grounds.

"Who knows what will happen. I'm not going to say we will win the World Cup, that would be ridiculous, but we might just surprise a few people."