The car is built by going near the 'assemble the car' panel and interacting with it with 'E'. If you are close enough and looking at it, it will show the green light indicating that it's ready for interaction. If you try to build without resources, it will show you the red light, otherwise the car is deployed. Probably you weren't close enough to it, was it the issue? In such case I guess I need to clarify the quest objective...