did any local tribal people live in the carribean islands before christopher colombus found the new continent?

there were 3 waves of settlement in our islands.....first the Arawak's, who were overrun by the Caribs, who were almost exterminate by being kept as slaves.....and a food source.....by the cannibalistic Tainos.....Columbus and the Europeans were the 4th wave of settlement

Yes, there is evidence of that. Mayans lived in the Mexican-American area, I think, and I doubt there was an entire continent opposite Europe, sitting, as empty as an anorexic's fridge.

Yes. the Tainos. Unfortunately their population was all but wiped out after the arrival of Europeans.

I think for the area of Puerto Rico they were (or maybe still are) called taínos