Biggest icebergs have areas roughly similar to Crete and 500 meters thick, (https://en.wikipedia.org/wiki/Iceberg_B-15) I assume most of that thickness is hidden underwater, sadly I could not find answer to how high above the water was the actual biggest iceberg recorded. Icebergs, being made of ice, do not survive well in hotter climates and often break into smaller parts. My idea is: create an iceberg out of pykrete (https://en.wikipedia.org/wiki/Pykrete) to decrease the melting problem, add internal tunnels with cooling equipment and structural support for the gigantic structure, and then, cover the iceberg with soil, rocks, trees, small hills, houses, everything you could find on a normal island.
I need to know if such island would be physically possible to build and if you could build an entire self contained ecosystem on its surface.
Edit: If you think other materials are fit to fulfill the requirement of making Crete-sized floating island, I am open for suggestions.