I played my first game of EU2 in ages this weekend, and for fun I took the Aztecs, just to see how long I could last.
I didn't realize just how bad the research situation was going to be. It was brutal.
Still - by 1819, I was ranked 7th in the world.
What I did -
First, I warred against my immediate neighbors - the Zoasomething or others. Three provinces immediately south. Took them and annexed them piece by piece in three wars.
Next, took out the Maya - which secured my place as sole country in Central America. Explored south down to Panama, and colonized.
Next, started moving north, up against the Rio Grande and the Navajo. I kept good relations with the Navajo but they kept breaking their treaties with me to defend each other - they had to die.
I kept Spain at bay, attriting large armies and taking theiir colonies - after a while, they had to take peace due to war weariness.
I also fought many wars against the Inca, but couldn't conquer them due to lack of cannon and such high attrition levels - just couldn't keep 10,000 troops alive consistently. Toward the end, they allied with me against Spain.
Biggest problem - halfway through the game, I no longer get leader changes, and the last one you are stuck with SUCKS. Bad.
This is straight up - no cheats, no tricks, no nothing. And very fun - just a little frustrating that with so little tech, no way to combat inflation or do much of anything else...
At the end of the game: