As a potent industrial power backed by a highly unified, militarist society, it was nearly a foregone conclusion that Paraguay was going to win the war of the triple alliance and achieve their territorial ambitions against Brazil, Argentina, and Banda Oriental (which back then was called Uruguay). Given a POD at most twenty years in the past, is there any way the triple alliance could have won without foreign intervention?
Bonus round #1: You can't include "Imperator Dom Pedro II never falls from his horse" as part of your POD.
Bonus round #2: The American war of Reunion never happens, so Brazil is able to continue trading with the CSA