Europa Universalis IV

With El Dorado expansion, create a custom nation (no more than 200 points) in the Caribbean. Give them Bahamas and another province in the same sea zone as the Bahamas. Make the nation Western Tech so you get ships. Then start the game and use your light ships to privateer The Caribbean. The event will fire and you can play New Providence as early as 1445. If Portugal or someone starts colonizing, let the Colonial nation form and attack them without Portugal defending.

My run England colonized Bermuda. I recommend going Expansion with your first idea set and grabbing that island before England, since they won't be able to form a colonial nation and you'll have to fight them directly for it.