FLINT, Mich. — The first car arrived around 3:30 a.m., more than six hours before the weekly “help center” opened at a local church. David Brooks, a 72-year-old retired General Motors laborer, was in the second car in the queue, and passed the time by sleeping in the back seat of his refurbished 1997 Chevy Santa Fe, as has become his Thursday routine since 2014 — the last time his Flint community trusted its water.

By 10 a.m., when volunteers at Greater Holy Temple Church of God in Christ began to distribute cases of bottled water to the gathered residents, the line of cars stretched more than a mile and a half. Inside the vehicles were parents whose young children have bathed in bottled water their entire lives, mothers who needed bottled water to cook food, and families still haunted by the prospect of disease and death, more than four years after the residents first sounded alarms about problems in their state-run water supply.

“They poisoned us,” Mr. Brooks said as he waited. He emphasized “poisoned,” the preferred word of residents keen to cast the crisis as a man-made calamity at the hands of state government.