I have an image of a start on a random map, it started me on an island that I can't get off.

While this has been reported a few times already he is deffinitly a winner for spawning on smallest posible island in Factorio.
For this I think he deserves some prize

Bad luck There is no check in the map generator, that the player has enough space. Just restart the game.

Start a small island with no possibility to move , may be a bug or just a tweak at the map generator