A $75 million animal shelter in Queens, the borough’s first and only public shelter, was supposed to boost adoption rates, making animals irresistible to prospective owners.

It had spacious kennels for dogs. A skylight in the adoption room. Dedicated rooms for cats to roam free. High ceilings and state-of-the-art veterinary facilities, including a dental clinic.

But before it even opened in late July, the shelter was already in trouble.

The 50,000-square-foot building, designed to accommodate 72 dogs, was tapped to take in 77 dogs displaced from a city-run Brooklyn shelter that closed for renovations. Councilman Robert Holden, who represents a part of Queens near the shelter, said he recently received photos that showed dogs penned in small kennels with shredded blankets and bedding, smeared in excrement, their water and food dishes empty and overturned.

Alarmed by the images, Mr. Holden went to see the facility, the Queens Animal Care Center, for himself.

He was greeted with an earsplitting cacophony of barking and the unpleasant odor of dog excrement, he said. The roof leaked, the ventilation was “horrendous” and “a lot of things don’t work in it,” he said.

The gleaming promise of the new facility had crashed into the messy reality of shelter work.

Rescue experts and animal welfare advocates say the situation in Queens is just one symptom of a bigger crisis: A steady stream of animals in need of homes coupled with stagnant adoption rates is pushing the city’s shelters toward a breaking point.

Just one month after opening, the Queens shelter’s dog population is at more than 210 percent capacity, and there are almost twice as many cats as there should be. Staff shortages have left the workers and volunteers scrambling.

The shelter, operated by the Animal Care Centers nonprofit system that runs New York City’s public animal shelters, was more than two decades in the making. In 2000, the City Council passed a bill requiring each borough to have an animal shelter. Finally set in 2019 for an industrial plot in Ridgewood, the Queens shelter was delayed for years by budget and zoning constraints, toxic chemicals in the soil and construction issues.

Still, excitement abounded as the opening day approached.

“We thought, well, it’s so great, it’s such a great adoption experience, that the animals will fly off the shelves,” said Katy Hansen, a spokeswoman for Animal Care Centers of NYC.

That hasn’t happened, and animals haven’t stopped streaming in. Currently, the shelter houses close to 160 dogs. Its kennels, designed to have two chambers for dogs to move between, have been divided in half to contain the overflow, Ms. Hansen said.

According to the terms of its city contract, Animal Care Centers cannot turn away animals, even when they are at capacity.

Ms. Hansen said the photos Mr. Holden described — which were published by The New York Post — don’t capture the complete picture of what it’s like for animals in the shelter and have put additional stress on staff and volunteers.

“We are making it work,” Ms. Hansen said. “And, you know, for every one picture you see of a dog in a dirty kennel, there’s 500 pictures of dogs in great condition.”

Still, Ms. Hansen acknowledged their difficult situation. “We’re in dire straits,” she said.

In June, the most recent month for which data is available, the three Animal Care Centers in Manhattan, Brooklyn and Staten Island took in 434 dogs, according to public records. That month, 108 dogs were adopted, 54 were euthanized, 216 were transferred to other rescue groups and 83 were returned to the families that surrendered them.

Rescuers say that the primary issue shelters face right now isn’t an uptick in surrendered or abandoned animals, but declining adoption rates, specifically for dogs.

“There’s people still adopting, but they’re not enough to clear the shelter, if you will,” said Christa Chadwick, vice president of shelter services at the American Society for the Prevention of Cruelty to Animals.

The skyrocketing cost of veterinary care and the rising prices of pet supplies are keeping some people from adopting. Some rescuers say the city should invest more in subsidizing spay and neuter services, which can cost nearly $1,000 in New York, to make them more accessible and stop the overcrowding problem at its source.

Recently, more animals coming into Animal Care Centers facilities have had behavior or health concerns, Ms. Hansen said, making it harder to find permanent homes for them.

“It’s a confluence of just terrible things happening all at once, and our shelters are not designed to house this many animals,” Ms. Hansen said.

The Brooklyn shelter is not set to reopen until 2026. The fifth borough shelter, in the Bronx, is slated to open next year, but will only accommodate about 70 dogs.

And the Queens shelter is still looking for more help.

It is hiring for 10 different jobs, including animal care specialists, veterinarians and veterinary technicians.