This kind of question can't be answered. It's such a simple gesture, no matter what date anyone gave, who could ever be sure that no culture or group ever waved before that?

It's a natural progression from raising one's hand in greeting, to waving. Perhaps it was for visibility - a moving object is easier to see from afar than a still one. Perhaps it was just enthusiasm - it's more natural to move than to be still if you're greeting someone because you're genuinely happy to see him. Who knows.