If the island had been long-settled by that time, a major migration from Egypt would have been unwelcome, but a few skilled craftsmen would have been accepted. They would have changed Minoan technology while not affecting Minoan genetics to a significant degree.
If the Minoans had come from Egypt, wouldn't they have spoken Egyptian? They could have had scribes keeping records with Egyptian hieroglyphs instead of inventing their own writing system.
Place names on Crete suggest that the people living there in the Bronze Age were similar to those of mainland Greece during the Early Bronze Age (before the "Greek-speakers" invaded). There are also similar names in Asia Minor so possibly the Minoans were related to some of the early Anatolian populations.