Civilization is a little difficult to define.
I am sure I read somewhere that the oldest palace in the world, or maybe just Europe was on Crete.
Greek myths which go back to the fog of the beginning of written history, imply that Greece was under the thumb of Crete.
Civilization means, building and living in cities. Easy definition.
The Minoan Thallosocracy was invented by Sir Arthur Evans or some other Victorian; the Mycenaeans took over later, and during the Trojan War, the allies from Crete went along. Linear B (from Knossos and other places, including Pylos in Greece) is a writing system that was used to record Greek, and generally thought to have been derived from Linear A, which is presumed to be Minoan.
The Attic Greeks claimed to have lived in Attica since before the Moon was in the sky, and of course the Platonic dialogues about Atlantis purport a longer existence for the Greeks than the Greeks themselves knew (the Egyptians claimed only that their records were oldest and continuous, at least according to Solon, allegedly).