When Christopher Martins insouciantly chips Luxembourg’s fourth goal, finishing a beauty of a move that he started 70 yards down the pitch, his manager turns away in mock horror. “Sometimes he’s too relaxed, too cool,” Luc Holtz explains of his reaction to a 21-year-old who has stood out all evening in the holding midfield position; Moldova have been disposed of clinically and now, at long last, Martins is not the only one who can loosen up a little.

More than that: perhaps he and his teammates can start to dream bigger. The Uefa Nations League has raised the stakes for countries like these, charging fixtures that would barely have raised an eyebrow with unprecedented energy. Luxembourg, 85th in the world, hosted 175th-ranked Moldova knowing that qualification for Euro 2020 no longer looks a wild flight of fancy. One of the 16 teams in League D will make it and, even if a fast-tracking to the highest stage feels contrived, it makes this by far the most interesting – and least knowable – section of Uefa’s new competition.

That is why Paul Philipp, who has kicked every ball from the stand during a 4-0 win that was anything but easy for an hour, puffs his cheeks out at full-time. Philipp, the president of the Luxembourg Football Federation, won 54 caps as a player and managed the side for 15 years. For most of that time their games were universes unto themselves, centred on damage limitation and pride.

He had described this one as “crucial” and now, the tension having dissipated, he is flushed with relief. “We knew this would be the most important game,” he says, before looking ahead to an away meeting, on Tuesday night, with San Marino. “A difficult game, but it could be six points from six. Then anything could happen.”

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Such sentiments have been rare where the national team’s fortunes are concerned but there are reasons for the optimism that has been piqued in the Grand Duchy. A wealthy state better known for its appeal as a tax haven is few people’s idea of a football power; nobody is given to outlandish claims about their prospects just yet, with only six competitive wins in 22 years prior to Saturday’s fixture, but their upturn in the last 15 months speaks for itself.

A year ago Luxembourg drew in France in a World Cup qualifier and struck the woodwork near the end. They have beaten Belarus, Hungary, Albania, Georgia and Malta since June 2017, also holding Bulgaria and Senegal. There has been a spring in their step since that night in Toulouse and a feeling, too, that none of this has happened by accident.

Luxembourg opened a national football school in Mondercange 17 years ago, centralising the training process for local prospects aged between 13 and 19. With a population of around 600,000, only half of whom have Luxembourgish nationality, every last drop of talent needs extracting.

“We had to change our mentality,” says Philipp, who aims to produce footballers good enough to play in neighbouring France, Belgium or Germany. “It’s difficult to persuade a player from Luxembourg to move abroad at 22 or 23, when he has a good job and can still earn some money playing football. The young players need to leave when they are 16 or 17 and aim to be professionals. This is a long-term plan.”

Thirteen of Holtz’s squad for the Moldova game spent at least some time at the academy; nine of his players are still eligible to play for the Under-21s. All bar seven play in foreign leagues and Luxembourg’s methods appear to be working. In front of a 2,956 crowd – three times the number a friendly iteration of this fixture would have drawn – they start slowly and should be two down before Kevin Malget heads them in front. “My players were a bit stressed, the pressure on them was very high from the public, the media and themselves,” Holtz says afterwards. “They are ambitious and know they can do something right now.”

In the second half they are carefree. The 20-year-old left-back Dirk Carlsen creates a goal for his teammate of the same age, the FC Ufa midfielder Olivier Thill, with perhaps the best pass of the week; Daniel Sinani, a 21-year-old forward from the Europa League group stage qualifiers F91 Dudelange, rifles a third and by the time Martins, on loan at Troyes from Lyon, produces his party piece Luxembourg are vibrant.

It is the first time they have won by more than one goal since 1972; the Nations League lets minnows try things on their own terms rather than sticking 10 men behind the ball although, as the centre-back Maxime Chanot puts it, Luxembourg “don’t play only to defend”.

Should their approach prevail against Belarus, who complete the four-team Group 2 of League D, a place in the play-offs for Euro 2020 will look realistic. The hope is that this positivity can be sustained.

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Philipp admits to having “mixed feelings” about the Nations League as a whole: he worries that nobody at Uefa has committed to making the European Championship spot a long-term carrot, and fears the stealthy ushering-in of a pre-qualifying competition for the smaller teams. “We have to be careful that it’s not the first step to doing that,” he says; Uefa have told him and his peers not to worry but trust, at a time when major powers barely conceal their disdain for the also-rans, appears brittle.

This time, at least, they can imagine walking out in Rome, London or Munich two summers from now. “It’s very interesting for a team like us – there’s a really big chance to qualify for a major tournament,” Chanot says. For the first time in modern football history, Luxembourg have a core of players who might not look lost on that stage.