For up and coming fashion designers, the Met Gala sparks both fear of missing out—and just plain fear.

Sander Lak, the 34-year-old founder of the high-end Sies Marjan label will find out how much on Monday night. For the first time, Mr. Lak will walk the red carpet in the museum on New York’s Fifth Avenue, alongside supermodel Doutzen Kroes in a dress he created for the evening.

Mr....