So I've tried all of the countries in WW2 and Cold War starts and made a list of those that start with exactly 0 units. I don't know how many of them (if any) are supposed to have no troops so I've listed them all just in case. I hope it'll be helpful.
Czechoslovakia, Luxembourg, Yugoslavia, Egypt, Tibet.
Luxembourg, Yugoslavia, Egypt, Tibet.
Andorra, Vichy France, Egypt, Tibet.
Andorra, Vichy France, Egypt, Mengjiang, Tibet.
Andorra, Austria, Czechoslovakia, Iceland, Luxembourg, Saarland, West Germany, Yugoslavia, Muscat & Oman, Liberia, Bhutan, Ceylon, Japan, Monolia, Nepal.