MINNEAPOLIS — Last year, with the federal government making available huge new sums of money for programs to feed needy children during the pandemic, a nonprofit organization called Advance Youth Athletic Development set up what it described as an enormous child care operation in northeast Minneapolis that could prepare 5,000 dinners each weeknight.

Based on the group’s claims, the State of Minnesota channeled $3.2 million of the federal food aid to the program.

But on a subzero morning in January, the F.B.I. carried out a series of predawn raids around the region. It revealed a sprawling investigation into Advance Youth Athletic Development and other groups like it — and the much larger nonprofit organization, Feeding Our Future, that was responsible for ensuring that the money provided to the smaller groups was spent properly.

In court filings, the F.B.I. said it had discovered a “massive fraud scheme” among groups that Feeding Our Future was supposed to oversee, saying they siphoned off tens of millions of dollars by charging taxpayers for nonexistent meals.

In affidavits filed in federal court, the Justice Department said it was investigating at least 15 different feeding operations. Together, the F.B.I. said, these groups — all of which were supposed to be overseen by Feeding Our Future — had received more than $65 million from federal food programs during the coronavirus pandemic.

“Almost none of this money was used to feed children,” the government wrote in one filing. “Instead, conspirators misappropriated the money and used it to purchase real estate, cars and other items.”

When a reporter recently visited the address listed for Advance Youth Athletic Development, there was no sign of a kitchen or a large child care facility. It was a second-story apartment.

“No. No. No,” said Lul Mohamoud, a neighbor in the apartment across the hall, when asked if she had ever seen 5,000 children there. “I have never seen any kids going in there.”

No one has yet been charged in the case, and the leaders of Feeding Our Future, Advance Youth Athletic Development and other nonprofit groups have denied wrongdoing.

But the case has highlighted how the government’s reliance on nonprofits to help carry out an array of programs can increase vulnerability to fraud — a problem that only increased over the past several years, as Washington pumped trillions of dollars into pandemic aid packages.

That aid has focused new attention on the role of nonprofits in particular in acting as conduits and overseers of federal money that flows through them via the states and then to smaller organizations that carry out programs. States and the federal government count on groups like Feeding Our Future to guard against corruption — even as the system incentivizes the organizations to push more money out the door by giving them a cut of it.

In his State of the Union address last week, President Biden said that “billions” in pandemic aid had been stolen, and that he would soon name a chief prosecutor for pandemic fraud.

In Minnesota, state regulators said that even after they grew suspicious of Feeding Our Future, they had been constrained by the courts from stopping the organization. In fact, the state paid the group more than $197 million after the first suspicions were raised.

“The scale of this, and the rapidity of it, is astonishing,” said State Senator Roger C. Chamberlain, a Minnesota Republican whose committee oversees the food programs. He said his goal was to understand “why this system failed and collapsed completely. Because it certainly did.”

In all, more than 200 investigators from the F.B.I. and other agencies raided 15 homes and offices around the Twin Cities.

The Minnesota case involves two multibillion-dollar federal food-aid programs, both funded by the Agriculture Department but administered by states. One pays for meals at preschools, emergency shelters and aftercare centers. The other pays for meals at summer activities.

In the 1970s, Congress created a role in both programs for nonprofits called sponsors, so that giant state bureaucracies and tiny day care centers did not have to talk to one another directly.

In theory, the nonprofit groups that fill the sponsor role make sure that feeding sites follow the rules, then hand out federal money to those that do.

The watchdogs can keep as an “administrative fee” up to 15 percent of the funds they pass along. Critics say that creates a perverse incentive: a reason for the watchdog not to bark. The structure, they say, rewards sponsors that pursue bigger networks and larger checks instead of those who crack down on fraud — a problem that has been evident for decades.

“Since the sponsor is essentially the internal control for this program, any disreputable sponsor could abuse the program with little or no chance of being detected,” the Agriculture Department’s inspector general wrote in 1998, after an investigation called Operation Kiddie Care found “fraud on a grand scale” in one of these programs. “In fact, the design of the program may encourage program abuse.”

The Agriculture Department declined a request to interview an official about the case. Instead, the department issued a statement saying that “it takes fraud and the protection of taxpayer dollars very seriously.”

Since the F.B.I. raids, news coverage by The Star-Tribune and Sahan Journal, a local nonprofit media outlet, has revealed that some of the operators of Feeding Our Future sites had criminal records, and that a former top aide to Mayor Jacob Frey of Minneapolis, a Democrat, was among those under investigation. The aide has denied wrongdoing.

Minnesota first approved Feeding Our Future as a sponsor in 2018. In its first years, the group oversaw only a few feeding sites — and, at times, seemed to struggle with overseeing itself.

In February 2020, for instance, the I.R.S. revoked the group’s nonprofit status after it failed to file an annual report for three years. (Feeding Our Future says that status was later reinstated, but the I.R.S. still lists it as revoked.)

In other filings, Feeding Our Future said it had a three-member board to provide outside oversight of its finances. But the man listed as the board’s president from 2018 to 2020, Ben Stayberg, a bartender and electrician, said he had been tricked into taking the job and had “absolutely nothing” to do with overseeing the organization.

“I had a friend, she was like, ‘Will you just sign, put your name on there?’” he said in an interview. “I was like, ‘All right.’” Mr. Stayberg declined to give the friend’s name.

When the pandemic hit, Feeding Our Future’s world changed.

School was out. Children were hungry. Starting in 2020, Congress poured money into the feeding programs and allowed the Agriculture Department to waive rules that had been put in place after previous scandals to make sure states watched the watchdogs. For instance, state officials no longer had to visit feeding sites in person to see whether they were doing what the paperwork said.

After that, Feeding Our Future began to grow rapidly, adding dozens of new sites to its network. Some of them were start-up nonprofits that had sprung up during the pandemic and never served food before.

From 2019 to 2021, the number of children in Feeding Our Future’s network increased to about 400,000, from about 4,000, according to state records. The revenue flowing through its network increased to $197 million from $3.5 million.

Feeding Our Future’s share grew to about $19 million, which its founder and president, Aimee Bock, said she spent largely on salaries for her 80 employees and supplies for feeding sites. She said she paid herself $190,000.

But there were puzzling features at some of the group’s new sites. In Minneapolis, two Feeding Our Future locations claimed to be running large child care centers out of the same small building — one feeding 2,000 children a day, the other 500, according to state records. (Ms. Bock said the state records were wrong, and she had never claimed that food was served there.)

Another operation, housed in the nearby Safari Restaurant, claimed to be feeding 6,000 children a day on its own — more than the total number of children living in the restaurant’s ZIP code. Ms. Bock said the children came from surrounding areas, because the food was appropriate for East African immigrants, many of whom live in the area.

Advance Youth Athletic Development’s site — the location that turned out to be a second-story apartment — had obtained nonprofit status in June, using a fast-track I.R.S. process for groups that expect to have receipts of less than $50,000 per year. The F.B.I. said that after the nonprofit partnered with Feeding Our Future, it asked for $730,000 in reimbursements in its first month.

A lawyer for Feeding Our Future said the group never had an accountant on staff.

Then came the F.B.I. raids.

“My entire house shook,” Ms. Bock said. On the morning of Jan. 20, she said she heard banging and then saw F.B.I. agents at her front door. “All I could see were the spotlight and three guns, and they were just shouting, ‘Get down here! Get your hands up!’”

In an interview, Ms. Bock said she did not believe anyone in her network had cheated the system.

But if there was fraud, she added, “every test we have in place and every protection we have in place didn’t catch it. Is it possible? Absolutely. And if they got one over on us, I will help hold them accountable.”

Guhaad Said, the leader of Advance Youth Athletic Development, said the state’s numbers were wrong.

“I don’t know where that number came from,” he said in a phone interview. “I don’t know where the 5,000 children came from.”

That number appeared on the group’s application to enroll in one of the food-aid programs, which Feeding Our Future submitted to the state.

Mr. Said said his group had served meals at the site but declined to cite how many. He blamed Feeding Our Future for the discrepancy.

“There was not proper oversight,” he said. “So people may have made some mistakes here and there. But there was no intention to go out there and waste government money.”

In Minnesota, state regulators had grown alarmed by Feeding Our Future’s growth and lack of financial controls by summer 2020, a spokeswoman for the state’s Department of Education said. It tried to stop payments for many of the group’s sites. But Feeding Our Future asked a judge to intervene, accusing the state of discrimination because of its work with African immigrants and saying the state had not proved any allegations of fraud.

If its payments were cut off, the organization told a judge, the results would be catastrophic, leading to bankruptcy, lost jobs and hungry children.

A judge ruled that the state had not taken the necessary steps to stop the payments. After that, Minnesota officials called in the F.B.I. and continued to channel aid through the group while federal agents conducted a nine-month investigation.

After the F.B.I. raids, Feeding Our Future was blocked from receiving state food aid. The group sought to formally dissolve in late February.

Minnesota’s attorney general, Keith Ellison, said on Thursday that he was conducting a separate investigation of the group to determine whether it had violated state nonprofit laws.

The state has also sought to cut ties with a second sponsor called Partners in Quality Care, which had supervised some of the nonprofits that worked with Feeding Our Future.

A lawyer for Partners in Quality Care said it was fighting the action and had no indication that it was under investigation. As of last year, Feeding Our Future and Partners in Quality Care together oversaw 53 percent of the money that Minnesota disbursed through these two federal aid programs.

But even after the F.B.I. raids, there are suggestions that some people are still trying to game the system.

Lily Crooks, who operates a small day care center in Minneapolis, said she had worked with Feeding Our Future and received about $30 per month for a year for the snacks she served her children. After Feeding Our Future was raided, she said, a new sponsor called to recruit her — and immediately offered a plan to fool the state.

What if, the woman suggested, Ms. Crooks told the government that her snack was actually a full meal instead? “We could call it breakfast” and make five times more, Ms. Crooks recalled the woman saying.

Ms. Crooks said she declined, and was disheartened by the offer. “They are watchdogs, right?”