The first priority is to acquire 100 Religious Authority as quickly as possible to get the Mitma reform (+1 colonists). Each province colonized is one less to take from the Europeans. Make administration the national focus, then rush Administrative technology 5 to unlock exploration and unlock up to two additional colonists. The player isn't punished for beelining this idea tree as the primitive nations do not use boats early game, and the trade nodes they utilise are relatively poor until the European colonies arrive. With the release of patch 1.18, the player can easily rush the early technologies as your technology cost modifiers do not become noticeable until the mid 1500s, allowing the player to start colonising towards the eastern Brazilian borders in order to embrace reforms far earlier than was possible in earlier patches.
The second priority is to conquer the nearby Andean kingdoms in order to gain religious authority at a faster rate, stockpile gold and form the 印加 nation. As the player conquers the nearby Andean kingdoms, it is recommended to try to get the -2 terrain penalty when possible due to the majority of the terrain being mountainous in order to weaken attackers and not shred the tiny army the player possesses initially.
It is also recommended to be prepared for sudden changes in fortune during the entire playthrough as the 印加 possess some of the most volatile and devastating events in the game.
Forming the Inca as Cusco
As Cusco, the player will have a number of advantages. Both the King and the Heir have very good monarch skills. The King is also a fantastic general, which will give an edge in early wars. The player will get events to found Machu Picchu / Cusco, which give bonuses to legitimacy until 1821.
The player can either rival with Colla, Wanka or both. The player has to either conquer southward or northward. It may be easier to attack southward and ally with Wanka instead (so do not make it a rival). The player may get quests to ally with Wanka. It is advisable to sign a royal marriage with Wanka and forge a claim on Macaya (if Colla is a rival) Try to conquer all of Colla or vassalize it. Avoid royal marriages with Charca, Pacajes, or Calchaqui as the player will be conquering them soon. Do not wait long after subduing Colla, and prepare to attack again as quickly as possible. The player is recommended to be more cautious when raising autonomy in newly conquered provinces as opposed to other regions in the game as raising autonomy manually will directly reduce the player's religious authority which hinders the speed at which religious reforms can be passed.
Another way to avoid this problem is to vassal feed. By feeding provinces to vassals and then annex them, autonomy can be decreased giving 5 Inti authority as well as putting provincial unrest to very low and manageable amounts.
If needed, the player can declare war without a casus belli if this causes a war with a weaker set of allies, although more often than not the player will find a mission that gives you the conquest casus belli on a neighbouring province. If the player conquers Charca, Pacajes, and Calchaqui, Cusco should be strong enough for Ichma, Wanka, Huayla and others to become vassals. Nonetheless, Cusco should be more strong enough now to conquer all the kingdoms to the North, even if they are in a unified alliance/coalition bloc.
There might be quite a few events that cause a sudden drop in stability, so it is advised to keep stability at levels 2-3 when possible.
Once the player has conquered all on the Andean kingdoms, 印加 can be formed, which will give free claims all over the Andes mountains, including uncolonized provinces. The player can plan not to core colonies in anticipation of this, and save on Admin power.
Form Inca as other nations
If the player has Aimaran or generic Andean national ideas they will change to Incan when forming 印加.
Colonizing South America and First Contact with Europe
Now that there are no more enemies to fight, focus on colonizing as much as possible, and getting prepared to reform religion. If the player has followed the earlier recommended strategy, they should possess 2-3 colonists that have been working away as the player conquered the Andean kingdoms. The player should attempt to colonize in such a way to lock down a large number of empty interior provinces inside Incan territory, so that they can be colonized later. It is also recommended to colonize in a way that gives the fastest access to the newly arriving European settlers in order to have the institutions spread through your empire, which by this point are incredibly restricting.
The player should also have been passing religious reformations as the game went on, allowing you to finish your final reforms within this time frame. Reforming the religion will grant an immediate 10+ technologies, allowing you to catch up to your new neighbours.
An event to accept the Huacas may fire, which allows the player to reduce national unrest until 1821 for the cost of stability and some legitimacy. After having conquered the Chimu, an event may fire reducing Admin and Diplo tech by 5% until 1821.
After Exploration, getting Expansion is a good idea to max out colonizing rate, however the player is advised to wait as paying full maintenance on too many colonists can be a drain too large on the players economy before it truly takes off. Another recommendation is Economic as the incredible number of gold mines the 印加 possess have the nasty side effect of steadily increasing your inflation rates.
Conquer South America
The player will be lucky to have any allies at all, states will see South America as too distant to justify an alliance, and those that are interested will most likely be hostile. Nonetheless, allies can help in wars against the colonials in South America, even to distract and hold down some of the enemies' forces might be useful. Allying with another European power would be best, and the second choice is to ally with some middling power like the 刚果 or 马里. It is highly recommended to support independence for colonial nations when possible, then backstabbing them later. It is easier to gain land this way as compared to fighting a distant European force at the same time as the colonial nation.
Since the player needs every single province in South America, everyone who holds territory in South America is on the hit list. That being said do not pursue a policy of direct aggression with everyone in South America, pick nations who the Inca can beat, and try and dissuade war with the others. Incan conquest is made easier by the fact that they do not get overextention from conquering colonial nations. Inca will have to win wars against every colony in South America, and probably with France, Great Britain, Brittany, Norway, 丹麦, and certainly 葡萄牙 and Spain/ 卡斯提尔/ 阿拉贡. Eventually, Inca will need a powerful navy to be able to blockade these powers to force them to give up territory. Inca's long coastlines and vast income, lot of which comes from gold, can ensure that they afford to build a lot of heavy ships. It is good idea to make a fleet consisting of the full combat width worth of heavies. This fleet should be able to challenge even the strongest AI navies and successfully stop them from bringing troops from Europe to Americas. Keep some European or Maghreb powers friendly so Inca can blockade 法兰西, Portugal, Spain, or 大不列颠 . Should any colonial nation in South America foolishly achieve independence from their overlords, destroy them immediately. However taking land from them will cause overextension. Don't forget to colonize Galapagos, South Georgia, the Falkland Islands and St Helena.