If you want to go crazy:
- start as a Mayan nation, I recommend Xiu, Cocomes or Yokotan
- form Maya (requires passing 2 reforms)
- fully conquer the Aztecs
- flip Aztec culture
- reduce yourself to <=100% warscore
- declare war on a Nahuatl nation and have them force you Nahuatl (100% war score before they uncon)
- take the decision to Adopt Aztec Traditions
- declare war on a Mayan nation and have them force you back to Mayan
After that you do the normal American native run, reforming your religion etc. You will need to do all 5 reforms again after the religion change! And don't finish the "Reforming our Society" mission on the first two reforms!
The result of this is that you get both the Aztec and Mayan mission tree with double the Sunset Invasion missions:
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...but if you want to go for a calmer and more "normal" run, after having played both, Inca first, and following that finished my first World Conquest + One Faith last week using the above strategy as Aztec-culture Mayan Maya, Aztecs or Inca make for the better choice over Maya, both coming with their own advantages.
Inca gets a good government (Andean Empire; allows you to improve your ruler stats by +1!), Inti has good religious boni, the position usually gives you more time before the colonizers swarm you and you can expand quite well. The only worthwhile starting nation is Cusco, imo, and it allows for a very fast conquest of the region. Reforming is much less painful than the other two, just requiring sitting around, which you will be doing anyway while waiting for the disease bringers.
As Inca I was easily able to finish the Sunset Invasion part of the mission tree, despite a very powerful Korea and a very powerful France.
Reforming as Mayan is a lot more painful, requiring quite some preplanning with truces and luck with alliance chains if you want to go fast, as the game gives away provinces depending on culture, religion and distance to capital - and usually to already existing nations. They are also limited to passing a reform every 5 years by a modifier that also gives war exhaustion and prevents you from buying it down during the time. Colonies are pointless before all reforms are passed as you will lose them just like any other province over 15+reform_stage.
Nahuatl is somewhat similar, truces are the main problem, but at least you won't lose your land randomly. Not sure if they have any limit to how quickly reforms can be passed, if not, with some preplanning and luck, reforming should be a breeze. Doom should not be too hard to handle unless you expand crazily before reforming. (...I wonder if killing natives in uncolonized provinces by walking over them lowers doom?)
Aztecs also get a good government (Aztec Empire; only requires Aztec culture!), which uses Tonalli (gained similarly to how Doom is surpressed, through war and battles) to give you different modifiers depending on which "deity" you chose, with the great 15% coring cost reduction probably being the best option unless you want to focus on converting, at which point the missionary strength deity is preferable. Switching is not too costly, Tonalli can be gained quickly once great projects are upgraded or through wars.
I don't think Maya gets any special government interactions.
Another advantage for Maya and Aztecs is that you can usually consolidate Mesoamerica before the Europeans get their grubby little hands all over it, and then quickly colonize towards and conquer the Inti nations after reforming, while, as the Incas, from my experience, Mesoamerica is already part of the yellow blobmonster by the time you get there. Then again, maybe I was just a bit slow. Mesoamerica has about twice the dev compared to the Incan land, though half of it is of a wrong religion and there are several culture groups present.
One potentially massive advantage the Aztec mission tree gives you (requiring playing them or Adopting their Traditions) is that they can use "American Frontiers", creating "Siberian Frontier"-like colonies (free, but you will get events for them that may cost some ducats) on all available spaces adjacent to non-colony land - for just 75 reform progress. With some well planned conquering of natives in North America as well as good placement of colonies, especially in South America, it is easily possible to (almost) fully colonize the Americas by 1550 and earlier. (Fighting North American tribes is truely the worst experience in EU4 though, it is just utterly atrociously unfun and painful with migrating OPMs and everyone constantly running all over the whole continent and reappearing to siege your land when you start to siege all their uncrackable level 1 forts...)
Inca on the other hand only gets some free colonies around their land in South America (requires killing natives in the provines), while Maya gets nothing in that regard.
Either way you start, I recommend conquering and colonizing South America quickly, preferably setting up colonies and conquering colonial nations in a way that blocks off the interior from the colonizers. Prevent the Europeans from getting strong colonial nations in the New World, because they will be a pain to deal with if their overlord ever declares upon you - and they will, if you aren't powerful yourself, because getting worthwhile allies is quite difficult with everyone wanting your shinies!
If playing with the American Frontiers decision, set up your land for maximum number of adjacent colonies and watch your empire grow with the click of a button!
A main problem is government capacity when expanding quickly, so, make sure you grab the White House and build it up. Of course, put Courthouses everywhere.
There is also a fantastic policy you get for completing Exploration + Infrastructure, giving you +1 dev (in all three categories) in every colonized province, highly recommend getting that, especially since Infrastructure is helpful with the gov cap issue and Exploration is pretty much essential. Imo you don't need Expansion if playing with American Frontiers, but if playing Inca, it'd probably be helpful to have.
Religious ideas is helpful as well in many ways - casus bellus against everyone you border, easily done by just popping down a colony, no unjustified demands when declaring holy wars, and a very valuable missionary, which are very limited for these religions, missionary strenght and tolerance of the true faith.
Aztecs are likely the faster, but Inca is definitely a good contender. Maya is alright, but feels a bit left out compared to the other two.