You, my friend, are making the assumption that being advanced means to be like Europe first of all.
In many ways, it is not that difficult: The Andes is easy, due to cultural factors (Mesoamerica never became as unified as the Andes did under the Inka), early development of civilization (the Norte Chico predated the Minoans by centuries) and how developed it was in OTL.
Here is a schematic of my suggestion: Make the Wari Empire develop writing and have it not collapse in the 9th century but just have a decline (similar to China's dynastic cycle.) Why the Wari? Because the Inka were too late and the Wari were in many ways similar to the Inka (they built a huge empire, a vast road network, had a similar economy based on the mit'a system, which they developed.)
Have the Wari conquer Tiwanaku and the Nasca by the 10th century; this will give them the basis of concrete (the Tiwanaku had geopolymers, which in OTL USSR were used for concrete) to help in the construction of public works and metallurgy, which in a few decades could lead to ironworking.
By the time the Spaniards come to Wari (the capitol city is also known by that name), they find
a printing, paper using, steel (or at least iron) using civilization which trades as far as the Tarascan state via sailing trimarans based on those of Polynesian visitors that are 30 m long and sewn together.
The Wari have advanced medicine such as skull surgery and anesthesia (cocaine), rapid communciations thanks to their road network and adoption of
talking drums from Amazonia and no homelessness nor famine due to their redistribution economy. They have a large standing army of warriors armed with slings, maces and spears tipped with iron. The Iberians do not stand a chance.