For about a year, Chris Smalls has stood almost daily near Amazon.com Inc.’s largest warehouse in Staten Island, N.Y., campaigning to bring the first union to the tech giant’s sprawling U.S. operations. A former employee at the facility, Mr. Smalls held cookouts and small rallies with supporters there, and spoke with employees on their way to work to promote the campaign.

The persistence paid off, with workers there voting this past week to form a union, dealing a surprise to the nation’s second-largest private employer. Mr. Smalls’s journey from obscure activist to successful labor crusader shows how Amazon may have underestimated him—a top executive once questioned his intelligence—and the gathering momentum behind a labor effort that had previously proved fruitless. The journey also illustrates the challenges that will likely continue to make such organizing campaigns difficult.