I think you have a possibility, but it should be in 1600, 1650 at the latest. Why? Because before this our Litoral(Parana and Uruguay river zones where really low populated).
What's my POD? Well, say that in the Portuguese Restoration War, they do better and capture the part I mentioned from Argentina, which is possible with naval support. Buenos Aires is really small at this time, Montevideo doesn't exist, so the only difficult city is Asunción. Suppose they conquer it, so that in the peace this part of the Viceroyalty of Peru is given to Portugal. The rest remain as part of it and with independence will become part of a more powerful Chile. Maybe we can see some people in Litoral move to Southern Buenos Aires, like the Boers creating their own country but I really don't know.
In the 18th Century, large numbers of Portuguese people will come to the American colonies, so suppose some will come here, especially to Buenos Aires, which will grow really fast as it gives access to the Matto Grosso, the Misiones and Paraguay. Here expect also that Northern Argentina will see some cash crops and also some African slaves together with Guarani ones.
At the time of independence this part of the country will have double population than OTL(remember is not the whole of Argentina). I believe that if the Brazilian independence happens as OTL, it would be too big. So suppose that it separates. Maybe from Sao Paulo state to the South it's the Kingdom of Platina and the other is the Kingdom of Brazil.
I see the Southern Kingdom more able to atract immigrants, and also more able to colonize Chaco and Patagonia, winning most of it, except for Neuquen and what's in front of the island of Chiloe.
But I see it becoming a republic by 1850/60. Then more immigrants start to come, especially like 2,5 or 3 million Italians. It would abolish Slavery by 1850, because most of it wealth would be because of cattle.
Then the destiny of the country depends on its culture and values. It can become 1st World or it can remain a 3rd World like Argentina. And the population would be something between 75 and 120 million inhabitants, putting my bet in 100 million.
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