Colonizers heading for the gold mines at Cuiabá in the early 18th century used the Panará River. They also used the Tietê River for part of their journey, but not between Sao Paolo and Porto Feliz.
Those seeking their fortunes in Cuiabá made an epic trek of at least
five months that pitted them against deprivation, hunger, rapids,
whirlpools, and difficult portages. They began by traveling overland
from São Paulo to the port of Araritaguaba (Porto Feliz) on the Tietê
River, which they descended in canoes to the Panará. This river
carried the flotillas southwest before they began a difficult
northwest ascent into the interior along the Pardo River and its
headwaters.
Source: David Louis Mead, 'CAIAPÓ DO SUL, AN ETHNOHISTORY (1610–1920)' (2010 dissertation)
Porto Feliz is not marked on the map but is about halfway between Barra Bonita and Sao Paulo. Source: Wikipedia
Earlier, in 1628, the
Spanish governor of Paraguay, Dom Luís Céspedes Xeria, descended the
Tietê River on his way to Paraguay
Source: Mead
With the Tietê in particular having a large number of falls and rapids, boats often had to be carried for stretches. Missionaries also used the rivers, sailing both up and down both the Panará and the Tietê. For example, in 1810 Father Manoel Ferraz de Sampaio Botelho descended the Panará "in search of converts". However, some the locals were not interested and Father Sampaio Botelho barely escaped with his life. Then,
On the Paraná River, some of the crewmembers abandoned Father Sampaio
and, commandeering one of the river craft, headed back to Porto Feliz.
The missionary followed them, turning back and ascending the Paraná.
Source: Mead
Also in 1810 (September),
Father Oliveira Bueno, his brother, Capitão Miguel, and a retinue of
men began a 21-day journey down the Tietê to the Paraná in three
canoes. Where the two rivers flowed together, they constructed a base
camp on an island in the Tietê River...and began attempting to contact
the Caiapó by dispatching canoes up and down the Paraná River.
Source: Mead
Later, the Langsdorff Expedition (1826-27), also took the Tiete - Parana river route. In 1838, however, an outbreak of typhoid devastated the region, killing
most of the guides and boatmen capable of making the trip to Cuiabá;
this effectively ended the convoys of canoes traveling to and from
Cuiabá
Source: Mead
Thus the river trade "collapsed' and a patchwork of roads was used instead.
Much earlier (1526-27), from the Río de la Plata end, Sebastian Cabot and Diego García de Moguer had ascended the Parana up to where it was joined by the Paraguay river.