Ms. Torres had been saved by two neighbors as floodwaters filled her home. She was dazed and could not get out, so the men had lifted her through a window.

Around the island, doctors have teamed to make forays into hard-to-reach towns in the interior, jumping in cars and sport utility vehicles with whatever supplies they could muster.

In Humacao, a municipality on the eastern shore where Hurricane Maria snapped sturdy trees in half like pretzel rods and flooded entire neighborhoods, teachers showed up at school the next day, unbidden. Fallen trees covered the courtyard. Mud caked the hallways and classrooms. They put on gloves and started to haul away branches. Eventually, cafeteria workers served up thousands of meals for the homebound and others in Humacao.

In the distance, several weeks after Maria, mountains that had looked brown and stripped of life after the hurricane now glowed green.

“We will put fruit trees over there, and plants there,” said Carmen Gisela Rodriguez, a teacher in Humacao, envisioning a tableau of shade and plenty in the school courtyard. Her eyes welled up. “Amid all this grew a culture of sharing.”

Ms. Velez said optimism had sometimes slipped away from her amid so many unsolvable questions: Where to find food. How to cook the food. Where to wash clothes. How to fix the gate, remove the mold, rebuild her back rooms. Suicidal thoughts came and went, she said. But she smiled and clasped her cheeks in astonishment when Tito El Bambino and a well-known salsa musician, Pirulo, his dreadlocks bouncing off his back, walked along the street and right up to her. Her son whipped out his iPhone, and she basked in their attention.