It might be the first waste incinerator the neighbours actually want next door. The shop at the foot of the Amager Bakke waste-to-energy project in Copenhagen is packed with families desperate to be among the first to try its unique selling point: the ski slope on the roof.

“I live so close by that I could follow the development,” says Ole Fredslund, who lives in neighbouring Amager, as he helped his sons Felix and Victor strap on their boots as the slope opened its lifts for the first time on Tuesday. “I guess 90% of the focus is on the fact that there’s a skiing hill coming, so in a way it’s very clever. Everybody talks about the ski hill to be, not the waste plant to be.”

Ten minutes and three magic carpet lifts later, we are standing next to three short fir trees at the top of a blue run, an artificial slope consisting of green and turquoise bristles. Through the smoke from the next door Amagerværket power plant, Sweden is visible across the straits and to the other side a wide span of central Copenhagen.

The idea of topping a municipal plant with an urban ski resort won a string of accolades for the Danish architecture firm Bjarke Ingels Group (BIG) before the first shovel was even lifted. Time Magazine judged it one of the most innovative 50 ideas of 2011. Two years ago the architectural model went on display at the Museum of Modern Art in New York.

The building is wrapped in a facade of aluminium planters which will later drip with greenery. In the original plan, the chimney was to blow smoke rings, one for every tonne of CO2 generated.

A woman on Copen Hill. Photograph: Ritzau Scanpix/Reuters

But turning BIG’s inspired architectural sketches into reality has been challenging, says Patrick Gustafsson, the project manager who was hired “to prove it is actually a sound idea and not just a fantastic idea”. “No one has ever done this before, and that’s maybe for a reason, I sometimes think,” he laughs.

Above the carpet lifts, workers in fluorescent orange jackets are still finishing the landscaping on the steeper black and red runs and on the button lift that will serve them.

“The roof is very steep, actually too steep for a ski slope. It has an incline of 45%,” Gustafsson explains. “You can’t just shovel earth up there, you need to find a way of anchoring it, and then you also have to anchor a ski surface, plants, trees. It starts to get complicated.”

The ski resort alone has ended up costing 92m Danish kroner (£8m). The first day of skiing is more than a year late and it is only a two-day preview, with the slope now scheduled to be finished by May.

Skiers on the artificial ski slope. Photograph: Mads Claus Rasmussen/EPA

The smoke ring mechanism has been put on hold, in part because Peter Madsen, the artist who helped design it, was sentenced to life in prison for murder.

Christian Engels, the chief executive of Copenhill, as the ski facility is called, says he aims to provide a condensed version of a holiday in the Alps: “The full package, skiing, apres ski, everything, boiled down into a three- or four-hour experience.”

People living in the enormous apartment complex 150 metres away were given advance notice of the two-day opening, so they had a chance to snap up the half-price tickets. But others have come from further afield. Behind me on the magic carpet lift is Ricardo Karam, a Brazilian who lectures at the University of Copenhagen.

“You need to get used to it,” he says of the dry slope. “But after a couple of runs, it’s really fun and I can imagine that once the whole thing is finished, it will be even better.”

A keen snowboarder, Karam has been looking forward to the centre opening since he arrived in the city five years ago. “The idea, it’s fantastic. I’ve been looking at this building and just waiting for years.”

Once I round the slope’s first and only corner, I accelerate towards a small ridge, only to discover that it is covered in black silicon paste that stops my skis dead and catapults me hands first on to the lacerating bristles.

“It’s like glue,” says Karam as he helps me up. “It’s supposed to help you slide better. When I saw you I thought: oh no, it’s already too late.”

At the bottom, Fredslund and his sons seem excited but also slightly disappointed. “It’s fun, a little bit short of course,” he says. “But we are already improving after just three runs.”