Yeah, I don't know if it's that bad, really. The Warrior isn't trapped—look at the minimap. Not being able to get a Scout out is a drag, and having to do all your exploring with just one Warrior will definitely drag down your early income from meeting city-states and whatnot. But it's going to be impossible to take, with even the slightest defense, until Astronomy at least.
Monument first, research Pottery, build a Shrine, then Sailing, build or buy a Trireme and start exploring. Put some spare hammers towards a Scout or something, maybe enough to build a Granary after the Shrine. Crank out as many Work Boats as possible while researching Optics. Pop out the scout, then take a crack at the Great Lighthouse—there's not going to be a lot of competition that early. Try to squeeze in a Cargo Ship somewhere, assuming you've met neighbors. Then Writing, Library, Calendar, Philosophy, NC. Having to build four Work Boats would be a nuisance—and I doubt you could afford to buy many of them—but once you got a Lighthouse up, you'd actually be doing pretty well. If you get God of the Sea, that's what, 4

2

1

per Crab? Beats anything on land. Plus you can wait a good long while before you have to research Archery/Animal Husbandry/Mining or build a Worker, just work your way up towards Compass. It's kind of a cool spot.
If you went Liberty, would it stick your free units in the city? Probably. So Piety or Tradition?