Elon Musk pulled off opening a brand-new car factory in China with breakneck speed, sending Tesla Inc.’s shares to record heights. A follow-up act in Germany faces potential speed traps.

Tesla, which in November outlined its German factory plan, in recent weeks filled in some details for building on a site outside Berlin. The new facility in the state of Brandenburg is slated to go up quickly, if not quite within a year’s time as achieved in China. Mr. Musk, though, is known for aggressive self-imposed deadlines that are...