First-time buyers are rushing to buy homes after a decade on the sidelines, promising to kick a housing market already flush with luxury sales into higher gear.

Tracking home sales to a particular age group is hard, but a series of data points form a mosaic of a generation of young people ready to buy: The number of new-owner households was double the number of new-renter households in the first quarter of this year, the share of first-time buyers is creeping back toward the historical average, and mortgages for first-timers...