Well without asuncion, which was an important rest and resupply center for those who arrived at the Rio de la Plata from Europe, attracted by the gold and silver of Upper Peru. Using the Plata Basin to reach Bolivia is not viable. The interior is very wild and has many aggressive and numerous tribes.
Not only these cities but including Buenos Aires (the second time, after the failed attempt in 1536) , Concepción del Bermejo,Santiago de Jerez and Ciudad Real.(and of course Corrientes, Santa Fe ans Santa Cruz). So the name "Mother of Cities" was the name was deserved. So either the Spain really goes in force, bringing an army to pacify the region, which is very costly. Or simply give up and consider the region too wild/costly to be tamed.
La Plata 1783 (So I would say that the blue part of the map will not exist. What would happen is probably the Portuguese controlling some coastal cities. TTL Buenos Aires, Colonia, Montevideo and Santa Teresinha Only Portuguese version.)
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Buenos Aires was founded in 1536 to prevent the Portuguese from extending beyond the Río de la Plata. During the period between 1560 and 1640, the portuguese versions of Buenos Aires, Colonia, Montevideo and Santa Teresinha would been made. They will be nothing more than fortress cities. If Portugal enters into a union with Spain, Spain will try to wrest these cities from Portugal (I don't know if the kingdom will accept it). If they can't wrest these cities from the Portuguese. They will encourage the Portuguese to start invading towards Potosi. But I don't think they will succeed.
Success will only occur with the expansion of the bandeirantes.They probably arrived at the same time as OTL, so around 1640 they will be in Rio Grande do Sul. But without the Jesuits, military instructors and Spanish weapons to help the defense of the Guaranis TTL battle of Batalha de M'Bororé will be a victory for the bandeirantes. They probably arrived in Colonia around 1680. From there, they will begin to expand throughout the Plata basin. They will probably spend the entire 18th century fighting, carrying out raids, building forts to control the region. In addition to making trade agreements with Potosí to have access to silver (if there are no trade agreements they will carry out raids looking for silver). Increasing Sao Paulo's strength well before OTL. With slaves and silver being sent directly to São Paulo. The city will explode in wealth . At the same time, you will distance São Paulo from the rest of Brazil. With the loss of Minas Gerais to the Portuguese crown, I don't see the bandeirantes being confident of the crown. A good part of the money they will earn will be in weapons to secure their cash cow, the Plata basin. You could even have a large migration of São Paulo people after the Emboabas war looking to found a key city(or a few) that would give control of the Plata basin to the bandeirantes. TTL Gauchos and Bandeirantes could very well be the same groups (or see themselves as the same group). Only with different professions (one produces cattle, another hunts slaves, another sells weapons, another smuggles silver, etc.). With the Plata basin being opened to navigation, a common identity is likely. From then on, it is difficult to say anything.