A train grinds to a halt, mid-journey, in Bakirkoy, Istanbul, in front a giant screen. The conductor and passengers hold their breath, praying Turkey hold on to their 2-1 lead against Austria. All of a sudden there is a huge roar: everyone on the train, outside in the fan park and from Green Lanes, London, to Gaziantep erupts with joy.

Turkey, showcasing their distinctive brand of chaos-ball, have booked a quarter-final slot thanks to their goalkeeper, Mert Gunok, pulling off a Gordon Banks-esque save. He turned to a delirious crowd and celebrated as if he had scored. It is bedlam.

After 16 years, Turkey are back in the final eight of a major tournament and the Netherlands await on Saturday. It has been a long time since Turkish fans have had anything to cheer about and expectations this summer were not high. After years of pain, supporters were reluctant to get burned again. Many had also been alienated by heavy defeats in pre-tournament friendlies, club rivalries spilling over into the national team due to the squad selection and the usual conspiracies theories that hover around Turkish football.

Even reaching the finals in Germany had not looked certain. But Vincenzo Montella turned around Turkey’s qualification campaign after replacing Stefan Kuntz last September, his team finishing top of a group that included Croatia and Wales. The Italian also guided Turkey to a first away win against Germany since 1951. It was a friendly but so was March’s 6-1 defeat by Austria, after which Montella was asked: “Are you considering resigning?”

Montella stuck it out and has spoiled fans with some of Euro 2024’s most exciting games. It has been an emotional rollercoaster, great for neutrals but agony for the supporters.

Against Georgia, Turkey delivered goal of the tournament contenders from the teenage sensation Arda Guler and Mert Muldur, survived a late onslaught that included one shot against a post and another off the line, then scored on the break with Georgia’s goalkeeper upfield. Kerem Akturkoglu – nicknamed Harry Potter – charged down the pitch, slotted the ball into the empty net and celebrated by waving an imaginary magic wand.

In the final group game against the Czech Republic, the scores were level, Czech pressure was building and a possible tournament exit was beckoning when Cenk Tosun scored a goal in the fourth minute of added time.

But there is method to the madness and Montella deserves a lot of credit, especially for his tactics against Austria. Ralf Rangnick’s methodically organised, gegenpressing side were supposed to tear Turkey’s shambolic defence to shreds. But Montella succeeded where the Netherlands, France and Poland had struggled, nullifying the press by adopting a direct style. Turkey outplayed Austria before the interval and although the second half was back to chaos, they clung on.

Montella took a risk in switching to a back three and having his defenders play direct to Guler, a makeshift false 9 tasked with holding the ball up. The 19-year-old rose to the occasion. Merih Demiral, picked because Samet Akaydin was suspended, scored twice, made 17 clearances and was man of the match. And all this without the suspended Hakan Calhanoglu, the self-appointed “best midfielder in the world”.

It has not been plain sailing for Montella, though. The highs of the win over Georgia quickly turned sour with a defeat by Portugal. The manager received brutal criticism from just about everyone in the public sphere. Think Gareth Southgate after the draw against Slovenia but on steroids. A weaker character would have crumbled. Even the Turkish pop star Mustafa Sandal weighed in, calling Montella a “puppet-looking sorry excuse of a manager”.

Montella’s insistence on playing without a striker, coupled with toxic conspiracy theories of “dark forces” deliberately sabotaging the team and players being picked based on club affiliation, almost sent Turkey over the edge.

Guler has taken much of the limelight but this is not a one-man team. Ferdi Kadioglu, a versatile left-back, appears to have developed a third lung, contributing defensively and creating no fewer than 11 chances at the tournament. On Saturday Kadioglu will face the country where he was born and which he represented at youth level.

Montella understands Turkey’s football and fan culture after two years as Adana Demirspor’s manager. “Turkish culture is very close to that of the place where I spent my childhood. I was born and raised near Naples,” he also said.

It is no easy task managing in Turkey where emotions often spill over. For years managers have tried to create a less volatile and more disciplined national team. Montella opted to embrace the passion. “Besides our formation, our gameplan and our tactics, I saw Turkish heart today,” he said after the Austria game.

Montella is going to have to tinker again, with Demiral and the midfielder Ismail Yuksek suspended and Calhanoglu returning. Calhanoglu has performed well in spurts and scored a lovely goal against the Czech Republic but the Inter player has not shone yet. “The Netherlands are a strong team but Austria were favourites as well,” the captain said. “If you play with heart and fight until the end everything is possible.”

Turkey will play in Berlin, the historical and cultural heart of Germany’s three million strong Turkish community, and the game will hold special meaning for players such as the Juventus forward Kenan Yildiz, the Galatasaray defender Kaan Ayhan and Calhanoglu, who were born in Germany.

Montella has united Turkey and those who were calling for his head a fortnight ago will be asking for statues in his honour if the team win again. The last time these two sides met the Dutch won 6-1. Just like Austria had. A sign?