A seismic event will hit Luxembourg’s football scene if the national team win in Georgia on Thursday and repeat the trick next Tuesday against Greece or Kazakhstan. The country will prepare to lose a trademark part of its football scene because Paul Philipp, the president of its football federation, will appear live on television to shave off the moustache he has sported for more than 40 years. Should it come to pass, Philipp will probably navigate a whirlwind of emotions and conclude that the ordeal was worth it.

That is because Luxembourg, ranked 85th in the world by Fifa, stand two victories from a place at Euro 2024, a statement that would once have resembled fantasy. At the start of the qualifiers their previous 56 matches on that stage had yielded 15 points; attempts to reach the European Championship or World Cup have frequently finished winless or pointless and, while not in the San Marino bracket, for decades they were regarded as one of the continent’s smallest fry.

Now Luxembourg has football fever. Big screens and public viewings will shoot up all over the grand duchy, whose population of 660,000 has rarely had a chance to enthuse this heavily over sporting success, in time for the playoff first leg in Tbilisi. They will flock to watch in Place Guillaume II, a major square in Luxembourg City; the scene will be repeated from north to south for a national event few could ever have confidently anticipated.

“The stress is setting in,” said Luc Holtz, the long-serving manager who has presided over extraordinary progress. Luxembourg’s steady improvement had been attracting attention, at least from those watching closely, for the best part of a decade but quiet development has exploded into concrete results. Although they were thrashed twice by Portugal in qualifying group J, they secured a double over Bosnia & Herzegovina, drew away to an impressive Slovakia and took four points against Iceland. Evidence arrived that, at worst, they could mix it consistently with Europe’s mid-ranking sides.

That is why nobody should write off their chances of overcoming two more. Luxembourg are certainly outsiders in a path C quartet whose final is fancied to pit Georgia, and the wizardry of Khvicha Kvaratskhelia, against the 2004 winners, Greece. But a glance at Holtz’s squad shows no resemblance to the gaggle of semi-professionals, complemented by a sprinkling who had made it in neighbouring leagues, who used to brace themselves for damage limitation.

They are marshalled in midfield by the gifted Leandro Barreiro, a 24-year-old who has amassed 133 Bundesliga appearances for Mainz and is Benfica-bound this summer. The tall and elegant Christopher Martins, who opted to continue his career at Spartak Moscow after demonstrating his pedigree at Lyon and Young Boys, should partner him.

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Mica Pinto, a left-back who plays for Vitesse, is another experienced head in a group that draws from Luxembourg’s sizeable Portuguese community and also comprises players based in France, Belgium, Austria, Bulgaria, Serbia, Bosnia and Herzegovina, Norway, Switzerland, Ukraine and Slovakia.

Up front, Holtz will continue to select Gerson Rodrigues, who is on loan at Slovan Bratislava from Dynamo Kyiv, even though the 28-year-old has assault charges, which he has denied, hanging over him. Rodrigues’s trial is scheduled to take place on 27 March, a day after the playoff final. Holtz recalled him last October, having dropped him for disciplinary reasons in the previous three games, as the prospect of qualifying for Euro 2024 through the conventional path grew more real. Luxembourg finished third in their group but Holtz believes Rodrigues, the country’s all-time top scorer with 20 goals, has the star quality that could see them through this month.

Luxembourg can thank the Nations League for their shot at the big time: their showings at that level, in League C, secured their playoff spot. When the Guardian visited in 2018, watching them begin life in Uefa’s new competition by overcoming Moldova, the opportunity that lay ahead was clear. They were quickly promoted from League D and the extra competitive action, outdoing sides previously deemed their peers, has ingrained a winning habit. From eking out results they became confident playing on the front foot.

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Much of the vision Philipp, a legend locally who managed the side between 1985-2001, spelled out five and a half years ago has borne fruit. Back then he spoke of perfecting a production line with Luxembourg’s national football school, established just after the turn of the millennium, producing youngsters who could make early moves to bigger foreign setups. Martins and Barreiro are among its products; so are David Jonathans and Aiman Dardari, who are on the books of Bayern Munich and Mainz respectively. The latter pair are in the squad to face Georgia.

Given their underdog status it is a blow that Danel Sinani, the influential former Norwich and Huddersfield winger, now at German side St Pauli, will be missing through suspension. The tidy attacking midfielder Vincent Thill and defender Dirk Carlson miss out through injury. But Kvaratskhelia is also suspended for Thursday’s hosts, returning for any final, and a team that have become confident in tackling sticky away fixtures can feel confident of negotiating another.

“We must avoid being carried away by emotions, myself included,” Holtz said. Doing so successfully would bring them one step from a qualification comparable, at the very least, to Iceland’s extraordinary feat in reaching Euro 2016. It would ensure Philipp must start readying the shaving foam, too.