Aw, I get it. Yes a cellar under a garage floor would be a large cellar.
I am a retired builder by trade. I have built lots of suspended floors. They are expensive to build because of the shoring and support structures. needed. The floors also need to be at least 6 inches thick and heavily reinforced. It may pay to have an engineer look at the design to make sure it will support a car or three.........
As a rule, root cellars have a quite high humidity and are not ideal for storage of any thing that may rust, or dried goods that should remain dry.
Perhaps, you could make only one fourth of it for a root cellar and put concrete or block walls for that room and a door to isolate it from the rest of the area, and leave it a dirt floor, then put in a concrete floor on the rest of the area and put in three windows and vapor proof the floor and walls then there would be a chance of having a storage or work area down there that was neither dark nor terribly humid. The walls can be painted on the outside with waterproofing and put a 6 mil plastic sheet under the floor. It would then be more like a basement and could be useful for many things.
To have that much space just as a damp, dark old root cellar doesn't make much sense to me.
Gardening at 5000 feet elevation, zone 4/5 Northern Utah, Frost free from May 25 to September 8 +/-