You probably need a the 19th century to go better for at least one of the major South American countries in order to create a powerful common market by the 20th century. For instance there is a paradox forums AAR where Chile becomes the world's premier land power and, through physical assimilation of Argentina, common market domination of Brazil and other surrounding states, and education/technology becomes highly attractive to immigrants and foreign capital despite the typical Latin American political turmoil. By the early 1900's, that population and industry is leveraged into developing a fleet to match, and under a short-lived fascist regime Chile successfully defeats a US military attempt to contain their aggression against neighboring countries; though the fleet is sunk/scuttled in the fighting with the superior US fleet.
I don't find the way things played out in the AAR incredibly implausible, it's just not something you can build from scratch; unity between South American countries would take a long time, a long history of OTL rivalry turned into ATL cooperation, to bypass. And that's just one factor, hitting the floor running with the Gilded Age/late industrial revolution is another aspect.
But as a summarizing point, I find it believable that political instability is not an insurmountable factor in establishing these parameters. Extremist regimes come along and temporarily alienate the common market and foreign capital, and are eventually toppled and the relationships are reputations are restored. Honestly, being all the way in South America I think would help a country survive extremist periods, by often being defeated from within rather than without and having restrictions imposed upon it by a conqueror. I think a Great Power could survive coups and restorations better than invasions and foreign restrictions.
So I would start, given this sub-forum's specifications, with the year 1900 and pick a South American country to turn into a Great Power and to build a South American bloc around.