The best way to play the Mexican states is luck, or wait until the expansion (even though it does not help Meso or South America much, the fact it improves North America does benefit Meso-America). I am waiting for the expansion to try and get the achievement (hoping that by then the process is less mind-numbingly boring than the Cherokee achievement).
You have to be careful trying to annex the NA tribes in the beginning as the attrition will render you with no troops and high bills (especially if the Southern US tribes still managed to be allies). You may be able to get a lucky PU with the Incas (but this is very lucky as you cannot force it until exploration). Also, you may be able to see the Southern US tribes without exploration (unfortunately, most of the time I play I end up seeing Huron for whatever reason). Essentially colonize as much as you can. You can feed your colonies to your vassals, but you have to be careful about the colonies disappearing (as the vassals tend to go bankrupt and then suffer revolts).
Lastly, your first encounter with the Europeans is 100% luck. Most of the time they will attack you before you can westernize, or even before you can defend after westernizing. Even if you manage to take their land, it gives you almost no war score (so getting a peace deal before they spam units on your shores is unlikely, as taking their land often makes them send more units). If you are lucky, you will westernize, christianize, and get an army that can fight the Europeans without them attacking (but this is very small chance. So, be prepared to waste a lot of time fast forwarding the game, just to restart when Portugal or Spain decides you should not exist.
DasWood could have gotten about 2x-3x as big with a bit of selective diplo-annexing and vassal feeding colonies (even sooner). With that said, surviving the initial colonization is a lucky feat in itself. ADM is key until you westernize, nothing else matters all that much. You can also try (as much as luck will allow), to kill your low ADM rulers. I would usually park them empty land, letting the natives attack them constantly. Sometimes it works well, other times it seems to do nothing.