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...