In 2013, Mr. Villig started Bolt, initially named Taxify, after dropping out of college and mustering the courage to ask his parents to let him use the few thousand euros that had been saved for his tuition. He had been frustrated by Estonia’s taxi service and didn’t expect Uber to become available anytime soon in a country that some Americans cannot find on a map. (Estonia is west of Russia, south of Finland.)

Raising money from his parents turned out to be easier than persuading venture capitalists to invest in Taxify. A few local investors, including alumni from Skype, ultimately backed the new firm. But Mr. Villig was rejected by dozens of others who figured Uber would squash him.

“It was just a taxi app in Tallinn; you couldn’t see it was going to be big,” said Rain Rannu, an investor in Estonia who was one of the first to put money into Bolt. As for Mr. Villig, Mr. Rannu said, “he was just out of high school.”

Bolt focused on working with taxi companies before switching to a business more like Uber’s: offering rides through a smartphone app and using unlicensed drivers. The company homed in on markets in Eastern Europe, the Baltics and Africa where Mr. Villig felt Uber wasn’t making a big effort.