The Tupi move south
From Tupi to Guarani
About a thousand years later, maybe about 1 AD, some of those Tupi people moved inland. They abandoned their traditional fish-based diet, conquered the local people, and became the Guarani. As the two groups became more separate, the Tupi language became two languages, and the two groups couldn’t understand each other easily anymore.
Farming yuca root
These people brought farming with them to what is now Paraguay. They farmed yuca root and corn and peanuts. Farmers used irrigation along sandy beaches in the big Parana river basin. They sweetened their food with wild honey, and hunted for meat.
Did they use pottery?
Like their neighbors in Brazil, they made and used pottery, but not to pickle fish. Like the Assyrians and Mycenaeans and many other people all over the world, they especially liked to capture women in raids. Then they could enslave the woman and make them make pottery.
About 1000 AD, Guarani people seem to have fought their way further up the Parana river valley, conquering their neighbors and seizing more land.
After the Inca empire formed in the 1400s AD, there were wars between the Guarani and the Inca (and the Mapuche) over the border land between them. Some of the Guarani settled down on land they had conquered from the Inca. Others brought plunder and prisoners back home with them to Paraguay.