I think that's only if you stay in the opening of the cave. You get a save crystal once you get in there, so I'm guessing that you aren't supposed to leave. I've never tried to though so don't take my word for it. I can test it out though for you (I never delete my save files). Back in a flash!
Edit: sora_lion_heart is right. On the right side of the cave leading out is a little place where you can climb up.
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