Nope, they didn't exist for the entire time. Greece was missing from the map for centuries; at first, it was a part of the Eastern Roman Empire (though a core part), then a part of the Ottoman Empire (an oppressed colony). Italy was split into disparate city states for the entirety of the Middle Ages and Renaissance. The city of Rome was held by the powerful Papal State (a much larger predecessor to modern day Vatican), but it was not interested in preserving "pagan" monuments (the same could be said about the Eastern Roman Empire).