HEFEI, China—Volkswagen engineers in one of China’s electric-vehicle hubs are looking to the country’s automotive industry for clues about how to speed up manufacturing and beat back local rivals in the world’s biggest auto market.

The German automaker has long been the number one manufacturer in a market dominated by gasoline-powered vehicles, but it has been losing market share as China’s market turns electric. It is now trying to figure out how to compete with upstart Chinese makers that can roll out good, affordable and highly digital electric cars—and do so in a third less time.