Paths to the goal:
1) Vinland introduces Eurasian tech, germs, and by intermarriage genes more effective at resisting disease, the first two we want to happen slowly but deliberately so that by 1500 a big difference has been made, the last item--intermarriage--should happen as much and as fast as possible.
There are a couple good Vinland TLs going on right now.
Drawbacks: Most of the "good" effect of the injections of Eurasian stuff is limited and restricted to the near vicinity of Vinlander contact; thus the majority of the Native peoples somewhat prepared are also drawn into a Vinland-dominated cultural sphere. The people of Vinland may be mostly Native in extraction all right, but culturally they are a kind of Nordic variant. I believe there would be some dispersion of tech and moderately improved disease resistance into societies on the periphery that identify daily as Native, speaking Native languages and with Native philosophical outlooks. But odds are they are still strongly Europeanized. And it will take time for even a strong and thriving Vinland colony to develop the motives and skills to range far down the coasts to contact the more highly developed civilizations of MesoAmerica. Very possibly, a hybrid Native dominated society might arise in the Caribbean, interfacing with a Vinlander-catalyzed northern trans-Atlantic trade route. (I predict chocolate would become a very hot trade good eventually!) Also there are civilizations in the Mississippi River valley systems that might get hybridized. But even the relatively mild sample of Eurasian diseases Vinlanders are liable to transmit (remember, they themselves are largely insulated from the Eurasian plague stew until the speed and volume of travel across the Atlantic picks up, then they too will be terribly vulnerable--not as much as pure-blood Natives, but one does not inherent immunity to a particular disease as such, just the naturally selected genetic basis of a stronger immune system, so as far as particular immunities go they only have them for whatever they carried over themselves or have recently had inflicted on them) will be liable to topple these civs early on and what grows in their place, which might take centuries, is liable to be a strongly Vinlander influenced hybrid society. Or it may not have recovered at all by 1500.
Much the same applies to the Mesoamericans--contact with Vinlander traders is liable to either involve no transmission of Eurasian diseases (because any endemic to the home pool back in the far northeast die out on the long sea voyage south and so there is no infection) or if something does jump from the intruders, it will lay waste. Probably not as severely as the Spanish infections of the 16th century and later, since there will be less variety and less virulence, but the initial effect of such infections will be bad. Nor will this bad experience give the Native people sweeping immunity--it almost certainly will help them a bit, but except insofar as they intermarry with Vinlanders, they will still be stuck with a limited set of immune system alleles. They will gain insofar as a few Vinlander diseases might become endemic and thus switch their immune systems over to micro-parasite resistance mode rather than macro-parasite resistance (against worms and so forth)--which however leaves them more vulnerable to those macro-parasites, which is draining of energy. Perhaps most important would be cultural preparation for such a disaster in the future, which the post-1500 Europeans can be expected to bring in mass.
It just may be that between having a very moderate preparation for virulent epidemics, cultural and otherwise, tech transferred by the Vinlanders--horses would be a big deal but the Vinlanders are unlikely to have full sized riding horses themselves, but ponies and other domestic animals may be a help--and possibly a political alliance with Vinlanders interested in preserving their trade contacts, all these factors may tip the balance to allow some MesoAmericans or other to resist subjugation. Or perhaps they do get subjugated but the balance of power is less unfavorable, and later rebellions, after they have suffered more dieback and appropriated more European cultural tools, pose a stronger Native system against a weaker European control system.
2)
Qhapac Inka's suggestion that we look into OTL Native uprisings that did happen and see what it takes to establish them as victors, holding their own territory and with sufficient access to the expanding global ruling Atlantic meta-culture's tools to hold their own as the Europeans circle back later with redoubled interests and resources to try to resubjugate them. The 1780s rising is interesting in that it happens to match up in timing with the American Revolution in British North America. Of course the US Patriots were as anti-Indian a lot of people as you could hope to find on the planet, but is there some possibility of a linkup? Probably not; even if the American Patriots burned passionately to aid their Native soul mates in the Spanish lands, they had no projection to do anything material for them. US Patriot strategy was to minimize the number of organized European empires they had to fight, as much as possible make the Revolution Britain's problem alone and to get the aid of as many rival imperial powers (France, Russia) as we could. The last thing we'd want strategically is to convince the Spanish that we are a threat to their own interests so they throw in with Britain; at the very least that could cost us some valuable smuggling ports through which the Patriots hoped to get vital supplies like gunpowder.
Still I suspect that if one fools around with timing and politics, one might find some such synergy sooner or later. If the Native revolt is delayed to say the 1830s and mixed up with the nation-forming periods of Latin American rising against Spanish power, conceivably the USA might get involved. Probably not; more likely would be if as with the Hawaiians, British interest aligns with the success of a Native state.
Again as with Vinland (or other early Eurasian contacts--from West Africa or from China or Japan or Korea) the strength to survive and play in the Westphalian system comes from hybridizing and intermarriage, and the "Native" society is not "pure," just somewhat distinct from a straight European settler colony. They'd have to substantially assimilate to European norms to be able to engage. We might have withdrawn peoples living in defensible fastnesses. But even places like the Tibetan plateau or the Altiplano are not defensible in the long run against determined European invaders unless the people there can match their tech to some degree. They might not need the very latest guns out of Vickers or Krupp if they can make their own rifles and ammo, and have sufficient numbers, sufficient advantages of knowing local terrain, tough defensible terrain like mountain approaches--and finally, if conquering their realm is not really worth while for any reason. But the only way to be really firmly and safely established is to be in the game, with a reasonably modern army (and navy, if there is a sea shore) and domestic industry to back it up. They can't independently replicate the entire process whereby Europe developed modern industrial tech; they have to appropriate it.
3) Early POD, ATL native societies that have the stuff OTL Native America lacked--draft animals, better metallurgy, endemic disease leading (after tragic decimations downtime) to a more immune modern population. Even without any of these stipulations, one might still have ATL civilizations that either didn't exist at all OTL or did exist but then died out like the Mississippian societies. A great many such societies actually did exist--the lower Mississippian peoples DeSoto encountered (and whose pigs, bearing disease and running feral, probably did in); other early accounts of voyages up the Amazon turn up references to populous and developed settlements that vanished before later centuries could confirm them--and only now are turning up in the archeological record. The second wave of Mississippians were killed off by Eurasian disease but an earlier wave of mound builders appear to have suffered demographic collapse due to overextension. Perhaps with an earlier start, or some ATL crop (including crops that were tried and used OTL before maize displaced them, but perhaps in an ATL get another chance) the extent of civilization along the Mississippi system is so great that despite DeSoto's pigs, what survives the collapse is still pretty formidable. Also--if Mississippian civs are so thick on the ground that they remain citified and with extensive agriculture even after a series of diseases sweep through them, then presumably the surviving populations have been exposed to a fair number of Eurasian diseases and won't die off so often in the future--they still will when something new comes along of course. But note Europeans don't exactly prosper when these virulent plagues come through their own settlements either. On the other hand, if the Mississippi were really heavily developed, it would have attracted Spanish attention earlier and they'd make their efforts there as well as MesoAmerica.
Now that might be a scenario--the Spanish try to conquer north of their early Caribbean outposts as well as west, splitting their efforts and slowing themselves down on both fronts. In both Mexico and the Mississippi valley systems the populations collapse due to disease, but it takes so long to consolidate their footholds that the fragmented societies up and northwest, and up the river, have time to stabilize and get organized to resist. Perhaps the Spanish are reduced to negotiating to allow missionaries in and make respectful trade deals, and over time the back country societies get strong enough to hold off all colonialists indefinitely.
Other variations on the theme I've seen recently suggest effective cultivation (on a greater scale and diversity) of the Southwestern Deserts of north America (mesquite, other crops, possible domestications of animals)--a scattering of strong civilizations in the OTL Empty quarter of the US Southwest (Mexican Northwest) might catalyze more centralized civs in California too, and they'd be situated in terrain the early European conquistadors might have trouble reaching.
One grand and bold attempt I've seen along these lines is DValdron's Thule in the Lands of Ice and Mice. An ATL development of cultivation in the Arctic of all places leads to the photo-civilization scattered all across the tundra. The author seems to have given up moving the story forward but I was very eager to see it move into modern times, because I believed that the Thule enjoyed the advantage of what I called the "Arctic Fastness," that is, Europeans simply are ill suited to going into the northern lands of OTL Nunavit and attacking civilizational centers there that can subsist on crops that grow where nothing European can live. There is extensive hybridization culturally and genetically even by the Early Modern period DValdron got to, but I think that while most Thule descended peoples would indeed be absorbed into Eurasian societies (Icelander, Norwegian, possibly Russian, maybe some northern Siberian peoples) there would remain a substantial area in the heart of the American far north that they essentially control, and in time the European political system would come to terms, recognizing an existing polity and dealing with it more or less normally, with embassies and so forth. And the Thule would, even in this fastness, adopt European technology and science and become such a nation as the OP asks after.
This brings us to the elaboration of 3) which is pretty common, more common than the tough problem of an America where there are no draft animals, to societies that do develop draft animals of some kind. These sorts of TL point out that if you want the Native Americans to give as well as receive in the matter of epidemic germs, it is necessary to have draft animals and the sorts of centralized concentrated populations they allow.