Blind luck my foot.
1. Get good generals and build up economy:
2. In my case I went quantity/aristocratic/offensive. I underestimated France's morale + discipline advantage and lost some battles, but won some too. They (amusingly) couldn't keep up in manpower though, and occupations cut down their staying power:
3. Not even 100 years later, I get the achievement:
4. End score and ideas:
5. Empire:
A few things here. First of all, some people have finished significantly faster than me, owing to a combination of not going Protestant, not going republic (and getting good rulers), and France not PU integrating Portugal. I started pretty late (almost 1700), and still finished with decades to spare, 32/32/32, and maxed ideas...LOTS of wiggle room here.
I thought united HRE would be a challenge factor, but no they were a joke fight and I easily snagged Holland in 1 war with minimal fighting due to some creative use of forts in French land. Nobody other than France even knew how to put up a fight.
What's "super early westernization", by the way? You really should be westernized well ahead of 1550, more like 1540 is on the late side. If you manage trade in Caribbean well you can afford enough early carracks to smash Europeans to bits shortly after contact (you aren't relying on French protection, you might even attack them for colonies and win pre-1600), so winning wars can start early and you can seize their colonies often (go ahead and blow up their trade fleets if you can too, limits pull from WETN). After that it's just a matter of colonizing, killing natives + CNs, and building up enough infrastructure to challenge Europe while catching up in ideas.
Jihad, rereconquista, WC (especially 3 mountains), Norwegian wood are all harder. This one isn't a pure cakewalk, but calling it luck-based is a reach.
Something like this, only faster because you're not a tribal gov't as Aztec and going Christian rather than trying be lulzy with animist, should do (note: westernization completed in 1539):
Look, I have been playing with Iroquis. Iroquis start with 4 provinces and unlike Aztecs none of these provinces has gold. In the beginning they have literally few ducats of monthly income (minus the costs). By the time Europeans appeared in Canada in 1497 I had like 20 provinces and was strong enough to count as one of the biggest economies from both NA and Europe (lol). And I am in no way veteran/pro
Iroquois and the other NA tribes can reform-teleport their technology up to close to Europeans and unlike Aztec in 1.7.3, they have ideas. Aztec gold means jack crap before westernization BTW, because they're pagan and thus gold is worth less than grain or any other good they have. If you go Christian while westernizing, then you get full money from the gold and the income skyrockets, but tribes get tons of money too and can take Aztec as well.
Also, NA tribes can, with judicious use of subsidizing vassals to use their colonist, using 2 colonies at once, and extensive use of monarch points on non-tech, own more than the entire 13 colonies region directly or indirectly before Europe gets a serious presence. So long as you know how to game mid-war vassal deals to switch allegiances of your enemies via navigating uncolonized provinces, NA tribes can get disgusting quickly. I had the great power malus practically on contact.
NA tribes can build up carracks after reforming too, and can similarly afford them, but due to reform and the fact that it's possible to have a land FL of like 80 even after reforming, you can probably just win on land instead too.