Assuming an object that falls off the island teleports to the middle top:
Make a hole in the middle of the island, push a rock into it, and watch as it continuously gains speed forever by warping back to the top and through the hole once it reaches the bottom, only to repeat said process.
Once enough speed has been acquired, uproot a tree and position it in such a way that an impact to the other side of it will launch you in a see-saw fashion.
Use this rock’s momentum to launch you hundreds of thousands of miles away from the island to see if there’s anything out there. If there isn’t, at least your trip to space could end with you finding an orbital Sea Curse.
If neither work, the ceaselessly falling rock will still be usable as an infinite energy generator in the future.