You assume that all members of EAM/ELAS were communists. They were not. Also, there really was a window for them to take over: after the Nazis left and before t

You assume that all members of EAM/ELAS were communists. They were not. Also, there really was a window for them to take over: after the Nazis left and before the Allied forces arrived they were practically the only armed force in Greece. However they chose to wait. Mark Mazower's "Inside Hitler's Greece: The Experience of Occupation 1941-44" is an excellent book on the subject.