You might check here
for more information. If you look at the 3/4 ton section, Ben and Alain have provided a list of ambulance equipment as of 1943. I have not been able to figure out what "1 box of surgical dressings" actually means. I assuming that it is not a medical chest - 4 litter patients doesn't leave much room for the medical chest - so it might have been something smaller. The 1944 medical catalog lists a "9751700 Chest, ambulance, airplane" but it includes a lot of stuff that isn't surgical dressings. There is also "9782500 Surgical Dressing Set" but it does not indicate the chest that was used. This set includes among other things (8) 4 oz jars of boric acid ointment, 48 small first aid dresssings and bunch of other stuff that sounds like would require a standard medical chest. I have not found any other reference to the Surgical Dressing Set other than being listed in the 1944 catalog. I wouldn't be surprised if the box of dressings reference is generic and simply means "keep some bandages available". In that scenario, the box of dressings could be stored in an ammo crate or ration crate or whatever was available (which is what I do). Certainly that would have happened after the first couple of months in theater even if there was a specific chest to be used.
Historical photos have not provided any insight as to what would have been included except each ambulance had its own stuff depending on what the driver and attendant wanted to keep.