Why should a glacial province be the best province you may ask? The feature of Kagyrgyn (#2440) is that the owner of this province has the unique ability to reach the New World directly with Diplo Tech 3. The Iberians and Berbers have to go into Arguin and Cap Verde first if they don’t want to wait for Dip Tech 7. With Kagyrgyn you don’t even need the 50% from Exploration Ideas to reach America.

If you want to make the most out of Kagyrgyn you should obviously start in the region. You can pick any of the Tribes with a harbor (Chavchuveny, Chukchi & Kamchadals). Do not pick Khodynt, because you have to build boats and you are broke.
You don’t start with Feudalism, so teching will be hard (Feudalism doesn’t spread and Renaissance spawns in a couple of years). You want to rush Admin Tech 5 for Exploration Ideas. Set your Focus on Admin and move to the province in the middle of the Tribes with a harbor, build your army to your force limit and rival your new neighbors.
Mothball your transports and send your lightships privateering (keep them in port while at war).
Declare war for Show Strength to farm Mana, if you have luck Khodynt will move to you, so you can farm them also. Repeat this process until Adm Tech 5 is in reach. If the truces are gone you should force vassalize your neighbours, so they will help to fund your first colony or you annex them if they are OUT of your capital/Kamchadal state (obviously don’t annex them if you are not back at Kagyrgyn). NEVER migrate to a province without a port (your ships will be fed to the fishes).

Unlock your first two ideas and start to explore and colonize Aleut. Your economy will suffer, so pick the Native Repression Policy to finish the colony as quickly as possible.

Game”crash” trick: Restart until you have one gold province either your first colony or in Siberia (both regions have a higher chance to produce gold)

After you finished Aleut, you must unlock the extra 50% reach form Exploration Ideas to reach the next province Kenai. From there colonize your way south into today Greater Vancouver (No Tech Natives are there) and then out of Colonial Cascadia into California.

No there are two difficulties in front of you:

• When to develop Feudalism & Renaissance and moving the capital: Kagyrgyn is obviously a ♥♥♥♥ place to develop, so is most of Cascadia. The best region for development on the West Coast is the Bay Area and Central Valley. The good thing is that even mil tech 3 is enough to stomp the natives
  
  
• Moving the Capital: If you have 5 provinces in a colonial region a colonial nation will form and Cascadia is quite huge. Put if you move your capital to the New World, you lose the chance to spawn Colonialism. Check the colonial regions and maybe vassalize Natives in Cascadia instead if you would otherwise reach the limit.

Mil Tech 3 is enough for your conquest. With Mil Tech 4 it will be a massacre

Game”crash” trick: Restart until you spawn Colonialism

After Colonialism spawned you should move your capital to the New World. While deciding where to move your capital, you should check the formable nations: Depending where you moved your Capital you can form:

• Alaska[eu4.paradoxwikis.com]
  
• Cascadia[eu4.paradoxwikis.com]
  
• Sonora[eu4.paradoxwikis.com]
  
• Mexico[eu4.paradoxwikis.com]
  
• If you move your capital again after some conquest you could form Texas[eu4.paradoxwikis.com].

If you have monkesque patience other tags at the East Coast become available.
Siberian Ideas are not bad per se, but the formable tags have more interesting ones.
The interesting thing is that you can’t form Colonial Nations as a horde, but as a tribe and become a horde after you formed a Colonial Nations. This is a really good strategy, because you can get Nahuatl as Syncretic Faith for MAX razing power with the right government reform. Use this to swim in Mana. If you decide to go for horde, you should form Alaska. Alaska has +2 Tolerance of Heretics (all Natives will be heretics) for you so you can maximize your Horde government without dying to rebels in no time.
Now the fun begins and you can start expanding like crazy into the Aztecs for nice Inflation & Gold. Explore further south to the Incas and start the same thing there. Your Inflation will skyrocket and so will your bank account.
When you reach Admin Tech 10 you can form a new tag.
WARNING: You lose your Old World Cores & your Subjects if you form a Colonial Nation, only expand in the new world after you formed a new tag. (You don’t lose your colonies in the Old World, you can start expanding directly). Start a colony next to the Manchurian hordes, so shifting culture to Jurchen becomes a possibility (for Banners). Do not form Manchu if you want to keep the Americas.
Clean up the Aztecs, Mayans and Inca and colonize your way to interesting target for your conquest. If you are a horde, taking down Ming should be your Goal.

When the Europeans arrive in the Americas you have conquered the most of the Mesoamericans and Incas. Additionally your tech should be in check thanks to your advisors sponsored by gold + razing.

Beringia [en.wikipedia.org]was flooded after the last Glacial Period for a reason: