The seats began to empty with around 10 minutes remaining. First a few, then in their dozens, and then in their hundreds and thousands: Bayer Leverkusen fans pouring down the steps, massing behind the advertising hoardings, separated from the pitch only by a thin yellow string of ­stewards. Waiting for their time. Waiting for the moment when they could no longer be held back.

“Ihr werdet nie deutscher Meister!” rival fans always used to sing as a taunt to their Leverkusen counterparts. You will never be German champions! Over the long years of no, the long years of nearly, the five runners-up finishes, the six third places, the splutters and the collapses, perhaps even Leverkusen fans began to believe it too. Now, as the minutes ticked away, and with a delicious irony, they sang those same words to themselves: a requiem to the old Bayer 04 being buried, a hymn to the new one being born.

At 7.20pm on a cool April evening, Bayer Leverkusen beat Werder Bremen 5-0 to become ­Bundesliga champions for the first time in their 120-year history. For all the ­pandemonium that ensued in the minutes after a final whistle that nobody could hear, the sprinting hordes and the red flare smoke and the vanishing green grass, perhaps the most poignant motif was the sheer number of grown men still ­sitting in their seats, quietly weeping. Still not quite believing in the dream, even as it was becoming flesh in front of their eyes.

It is hard to visualise something that has never physically existed before. Even now, with the deed done, it is hard to know what to make of this wonderful Leverkusen team, with its paucity of household names, its modest budget, its century of historical baggage, the underdog club owned by the pharmaceutical giant with the £41bn annual turnover.

Played 29, won 25, drawn four. Bayern Munich, champions for the last 11 seasons, not just dethroned but defenestrated. Even the all-time Bundesliga points record – set by the treble winning Bayern side of 2012‑13 – is under threat. Where did this come from? Where does it go? Perhaps any attempt to process the scale of the achievement has to begin with that sense of sheer incredulity, the shredded logic, the shattered expectations.

Even as the Leverkusen fans gathered in the afternoon sunshine on the road now temporarily rechristened Xabi-Alonso-Allee, carrying their flags and flares and cardboard models of the Bundesliga trophy, buying their celebratory scarves and T-shirts, there was still a kind of unreality to the afternoon. The names on the replica shirts – Son Heung-Min, Michael Ballack, Kevin Volland, Bernd Schneider – evoked a different and yet more familiar age, every shirt a slice of the past, a memory of a team who never quite made it.

Regulars at the BayArena had never seen the surrounding streets this crowded three hours before a game. In a way this is the Bayer condition: a club fighting not just rivals on the pitch but a wider apathy off it. ­Striving to be taken seriously. To be seen as real. Leverkusen, let’s be honest, is not much of a real town. A giant aspirin factory with a football team and some square houses attached to it. Twinned with Bracknell, which feels about right. A place that does not begin or end, but just sort of dissolves into the fringes of Cologne, a city that does not care about it in the slightest.

Largely because of Bayer’s corporate patronage, Leverkusen inspire little wider affection among the ­German football public. The plastic tag continues to pursue them. So perhaps the greatest achievement of Alonso’s team this season has been to produce something so incontestably human: so obviously the fruit of real ingenuity and real effort, real passion and real pain. Youngsters such as the excellent Florian Wirtz and the irrepressible Victor Boniface have had breakthrough seasons. Relative veterans Robert Andrich, Álex Grimaldo and Granit Xhaka have pushed the outer limits of what even they thought they were capable of. Sixteen different players have scored a league goal.

Afterwards, soaked in celebratory beer, Alonso warned of the challenges to come. A Europa League quarter-final to win. A DFB-Pokal final against Kaiserslautern next month.

But as dazed fans filed back through the park and the fireworks popped over the chemical factory, nobody was thinking too hard about any of that. A new reality was taking shape, a separation of past torments and present fantasies, between the Leverkusen that exists now and a Leverkusen that will never exist again.