When you start on a real small recource scarce continent...

[Artifex1]

When you start on a real small recource scarce continent... maybe 1 luxury resource and another city state has another luxury resource...literally so bad you have no reason to found any cities other than your capital.

and the rest of your adversaries are on a large continent across the ocean with the rest of the good stuff.

At what difficulty level is that nearly impossible to overcome?

Would you usually restart in this situation?

 

[Glassmage]

Go Tradition and beeline Astronomy? Also go Honor and Piety (for happiness through certain buildings) and be a builder until you can go to other places.

 

[Babri]

I won't restart the game. Instead I would try to build some military & conquer that CS. Then I'll try to beeline astronomy & try to build a lot of wonders to overcome the loss of RAs & selling luxuries. Once other civs are discovered I'll plan to take other continents one by one.

 

[Drago Askani]

Or you could go for a fast 2-3 city culture win. Monarchy and hanging gardens for a super capital. Should be doable on quite a few difficultys I would imagine. After all your island nation would be fairly easy to defend especially later in the game with a few subs.