When the first Tupi people expanded their territory from Central America to reach the coast of Brazil about 900 BC, some of them kept on moving south along the Atlantic coast. About a thousand years later, maybe about 1 AD, some of those Tupi people moved inland, abandoning 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 – Tupi and Guarani.
Guarani people brought farming with them to what is now Paraguay. They farmed yuca root and corn and peanuts, using irrigation along sandy beaches in the big Parana river basin. They sweetened their food with wild honey, and hunted for meat. 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, so 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 Guarani settled down on land they had conquered from the Inca. Others brought plunder and prisoners back home with them to Paraguay.