Challenge/WI: Portuguese Empire monopolizes colonization until ca. 1600?

Historically, the Portuguese had a clear head start in the overseas colonial game, developing the caravel, exploring Africa and India before anyone else, and building a vast, trading empire despite their small territory and population.

What if their rise was even more meteoric?

Let's say John II of Portugal had accepted Columbus's request for a western voyage in 1485, and Columbus sets sail in 1488 for the Portuguese crown.

If Spain didn't have their lucky break and discover the Caribbean, the launch pad for their conquest of Mexico and Peru, they wouldn't really have had a position to challenge the Portuguese abroad. IIRC, all the Spanish had at that time in terms of Atlantic possessions was the Canary Islands.

Instead, the Portuguese would conquer the Aztecs and Incas. With that and the early settlements in Brazil, they would have a valid claim to all the initially colonized parts of the Americas.

Considering it took until the 1600s for anyone but Spain and Portugal to really start colonizing, could Spain be distracted by the Turks and Central European conflicts, while Portugal reaps the riches of the New World and the East Indies almost entirely on their own?

With the cash flow from the gold and silver mines in Mexico and Peru, and no European distractions, just how big could this Portuguese Empire get?
 
First off, why are we assuming Portugal is even able to conquer the Aztecs and Inca's? Cortez not only had a large amount of luck, he was also an experienced Conquistador leading other experienced Conquistadors. This played a key role in the Conquest. Portugal on the other hand has been out of the Reconquista game for centuries. Furthermore, even if they do manage to conquer, Porugal is a tiny country. There's a reason their OTL "empire" was made up of mainly tiny trading posts. They just don't have the population and resources to hold lots of land. How are they going to enforce their domination?

Also, if Portugal finds the New World, Spain is immediately going to do all that it can to get a piece of the pie. This is not because of the prospect of conquest but rather because of direct access to Eastern markets. The amount of Spanish expeditions sent to the new world picked up significantly once the Spanish knew for sure that Portugal was now getting rich off Eastern products.
 
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