I constructed the Elevator multiple times without problems.
If your game is not broken, it should work the common rule. That's it, you need a depot with the resources for the construction, the elevator, and a drone controller (drone hub, rocket, rover commander, etc.) with drones linked to the drone controller all in the area of the controller.
So, according with the priorities, the drones should do the works, and if you have drones without a higher priority task, and resources available, they should get that work and add resources.
My hypothesis is that, although you have resources, they aren't in the range of your drone controller, or your drone controller has no drones under his command, or the controller is off for some reason (maintenance, electricity, some event, etc.)
Of course, a bug is always possible, but construct a building is a very common thing I doubt it only occur with the underground elevator.