Bibek and Malati Rai in Queens, where they looked for a two-bedroom apartment for less than $400,000. Mimi d’Autremont for The New York Times

Five years ago, Bibek and Malati Rai found themselves at the same Sakela festival in Jackson Heights, Queens. Ms. Rai performed a traditional dance at the event, a biannual celebration of nature and heritage for the Kirat Rai community of Nepal and Northeast India. The two spoke only briefly, then crossed paths again at another community event the following week. But it would be a few months before Mr. Rai formally asked her out.