MONT-SAINT-GUIBERT, Belgium — The migrants while away their days in Brussels at Maximilian Park, near the busy Gare du Nord, playing soccer on the durable artificial grass, checking their smartphones, dodging the police and trying to find a way to Britain.

Roxane Hauzeur, a designer for a fashion house, began volunteering to help them a year ago, working with a new organization that provides housing and other assistance for the migrants, most of them from Africa and seeking asylum.

She found herself swept away, transported.

Ms. Hauzeur started bringing food, then giving rides, but soon she was playing host to up to five people a night in her small Brussels apartment. The experience has transformed her, she said.

“It was like a tsunami in my life,” she said. “You come and meet these people and you realize they’re just like you.”