It wouldn't have taken the Spanish so long to get to Mexico. Once the population of the Caribbean islands dropped to the point that hunter gatherer strategies paid better than farming, the Spanish ability to enslave servants would have disappeared. No slaves, no Spanish. They would have searched for easier prey. And brought smallpox to the Aztecs before they reached them so they would not have succeeded in conquering the capital city in the middle of the epidemic.
Think Latin America not being Latin at all. Possibly not any of America. They needed a labor supply to get established enough to bring over slaves, and a population density great enough that the slaves don't live by hunter gathering without being attacked by the natives. The natives don't resist you moving in until they get hungry.
No Indio slaves, no African slaves, no European colonies.