Missouri is moving quickly to try to win the first Hyperloop certification track, betting the nearly half-billion-dollar project will help turn the state into a technology powerhouse that can attract top talent from across the country.

Los Angeles-based Virgin Hyperloop One sent out a request for proposals Monday asking states to bid for a chance to host a 6-mile certification track that would test for commercial use the theoretical technology aiming to move people and cargo in near friction-free pods that can travel close...