The AI seems pretty nonchalant about colonizing at first, so it might be possible to colonize the east coast before the Europeans even arrive in North America. Of course, the danger of such a strategy is that France or Britain or whomever may somehow fit a colonist in there before you've gotten the achievement and then quickly declare war on you and dismantle everything that took more than a century to achieve.
I played one game as the Cherokee and my strategy was to simply wait for the Europeans to arrive, since I didn't think that I could reach admin level four in time. But no, France didn't place its first colony on the east coast until something like 1570, so I probably did not play a very optimal game.
Another thing I found is that westernization is a far more arduous process than in EU3, because you have to boost your stability back to positive before you can begin the process of fully westernizing. The resistance to westernization events alone are pretty terrible, but then the game decides to auto-convert me to Catholicism, which leads to religious riots everywhere and drops my religious unity to zero. Stability boost now costs about 300 admin points. My manpower is gone. I've taken out nearly 20 loans. I survive the entire ordeal, only to find that the neighborhood bonus on tech is a pathetic 25%, which is in reality 15% at most because of the tribal democracy penalty. So it might be 1700 before I can catch up in technology. I'm still debating whether I should have gone with one of the administrative ideas first, which would have allowed me to reform my government shortly after westernizing.