The only way to do what you are describing it to build it in place. Cabinet makers generally do no make the sides floor to ceiling for this reason and a few others.
You generally do would want a recessed toe kick for something like this rather than just a bottom shelf resting on the floor, which both looks bad, and functionally doesn't allow much of an opportunity to shim or scribe to any out of level floor.
The same goes for the ceiling, which will undoubtedly not be straight or level over any sizeable distance. So if you desire a built in appearance, you should design the shelf to incorporate scribes where it meets the walls, floor and ceiling.
Furthermore, if you build this completely and then install, you will need to be able to stand it up in place, and this means that the longest measurement from corner to corner will need to clear the ceiling, Building a separate toekick will give you a head start here. If you have 6" baseboards, and thus build a 6" tall toekick separate, then you can stand up the shelf, which will be at least 6" shorter before it is set on the toekick. Also, you can level your toekick first, and then run baseboard around it, and shoe mould to cover any gap at the floor.
Then you just need to address the scribe at the ceiling. If you build the shelf with a faceframe, then you can account for scribe in the top rail. Otherwise you could add trim, either overlay, or recessed. If recessed you can create a reveal which would make any trim at the top sort of disappear into a shadow line.