Inside a moving elevator using first-person animated camera on the matinee.

Greetings everyone!
My intention is to make a scene where an animated camera in the matinee, is in first person inside a moving elevator going up, simulating a person’s head. At first I thought of the simplest way to do it, that is, I animated the camera in the matinee and tried to attach the body of the elevator in the camera, so when the camera started its animation vertically, it would take the elevator together giving the sensation of being inside of this moving elevator, because the two would be running the movement together, the camera would carry the elevator. It turns out that when attaching the camera to the body of the elevator using the (attach to) command, it does not follow. How can I perform this action?
Thankful.