So in terms of the Inca, think quite possible that they survive for a while, manage to use defensively their mountain home. But people are getting ahead of themselves. Pulling a Meiji didn’t happen to societies a few thousand years ahead of the Inca. We probably came closer to 0 than 2 Meiji’s to be frank, Japan had one of the largest populations and by far highest literacy rate of the non-European powers of its day. Change is hard, requires determining what the correct measures are reliably is hard, Europeans succeed in large part because they are doing 1000 different things better. And elements in society will hate this. Just look at Madagascar or many other states. Attempts to modernize as often weakened as strengthened.
Now in what I think are more realistic terms, here is what may happen: The Inca will have several problems. They can hold interior, but Spanish will be able to build coastal forts that are impossible for them to take. European coastal forts were a problem that even states with semi-modern armies like Indian states tended to have huge problems with. So Lima, and a bunch of cousins. Realistically the Inca will have only 1 trade partner. Spanish didn’t have much competition in Western Pacific until well into 1700s. Incas are not going to get anywhere near fair market value for their gold. This though will still cause huge economic distortions. I expect resource curse issues. Wealth becomes much more about controlling and exploiting gold mines than the economy of the rest of Inca-land.
Disease will still hit *hard*. I think people overattribute the role of the Spanish. Plenty of groups saw population drop (Amazon being most extreme). It also takes a long time for bottom to be hit or any rebound to start. It isn’t so much like the Black Death as a series of them. Besides the first smallpox outbreak in 1528 (some other diseases may have been mixed in to, which may have killed 50%, over the next 100 years there were typhus, influenza, diphtheria, and measles outbreaks. Plus a second outbreak of smallpox. OTL the population may have dropped from 12 million to maybe 1.5? million in the 1600s including areas now in Chile and New Granada rather than Peru, then a final pandemic in the early 1700s reduced that to 600,000 in the districts counted. Maybe 1 million total OTL by then???
Assuming Spain follows broadly similar course, which seems reasonable, will be getting slightly less new world gold (but still all Mexican and good chunk of Andean), but still a lot. By the late 1500s, the Spanish initial wave had chilled out. Majority of the drop will have occurred by then, maybe 2 million for population accounting for loss of some peripheral areas. If Incas make it to here, I think good odds make it largely intact to 1700s. Then come the Bourbon Reforms in the 1700s. This is another risk period. European states are sending larger forces overseas. By this time New Grenada and Chile (hard to believe isn’t settlement between Mapuche and Inca power centers) are getting big enough to contribute significant numbers of militia. If they are unlikely the Spanish decide to add the gold source to their realm. If they are lucky maybe the French or British seize some of the Spanish coastal cities to get trade access (though that or fear of that could also encourage Spanish conquest). Then come the 1800s. This is probably when they finally go down if they haven’t. Repeating rifles and such meant Europeans were finally able to crush with devastating easy even previous hard nuts. Pretty much everywhere in the world became directly ruled or a vassal of Europeans and unfortunately for the Incas they have gold and silver.
