The big question is - why? American settlement at the time was almost entirely concentrated in Brazil and north. The first Spanish settlement that far south would be at the end of the 17th Century, over a hundred years later. And why not, say, Newfoundland or the North American East Coast, which is similarly unsettled but much, much closer to home.
I mean, it could be done, and maybe successfully (though any colony at the mouth of the La Plata would probably get subsumed)...
The first Spanish settlement that far south would be at the end of the 17th Century, over a hundred years later...
Actually, Buenos Aires was founded in 1536. It was abandonded a few years later, in 1541, after the colonist experienced hunger and Amerindian attacks. Survivors established themselves in Asunción, modern day Paraguay. It was from Asunción that Buenos Aires was founded again in 1580.
They did try to settle the North American East Coast, though. In Florida. Where they were killed by the Spanish.