So you want to mess up history, you say. So you want to not be racist or Orientalist or anything like that; to do something original. What do you do? Pull a Meiji.
So You Want To Pull a Meiji?
Here's how it's done.
'#1:' Find a country, preferably exotic, with a lot of wasted potential. On the world stage, Pulling a Meiji is the blue ribbon in the "Most Improved" category. It's just as blue as any other, it'll get you a round of applause just like any other ribbon, and it makes you a rising star - but you have to both need and earn that improvement in the first place. Before you try this, make sure you actually can get off the ground.
#2: Topple its authorities and install a new order. The ancien regime is currently ruling a country with a lot of wasted potential. They're okay with that, and if they're not they're only going to be willing to reform enough to keep themselves on top of the totem pole where they've always been.
"But what if I'm on top of the totem pole?" I hear you say. In that case it's more complex, because you're not just facing reactionary subordinates; you probably also have underlings calling for modernization and your head on a platter. Crush your underlings if you must, but by any means necessary get rid of your subordinates. Try coopting the revolutionaries; failing that, embrace them, legitimate them, and agree to become a figurehead. It may be a step down, but you can't have a say in the future when your head's on a platter.
#3: Make as many foreign friends as you possibly can. Send the children of the new order's leadership to every country that's less backwards than you, even if they're almost as backward as you. (Their familiarity with the regions will help you exploit them later, and their presence boosts your visibility now.) Send them to learn - finance, science, engineering, and militaria for starters. Send them far and wide.
Social engineering is half of it: the more places you have friends, former mentors, alumni, enrolled students, drinking buddies and whatever, the more you can interact with the rest of the world, and they with you - which makes it easier to attract venture capital. Much less obviously, but much more importantly, diversity gives you options. Overfocus, and you'll look no different from a built-up colony. Be eclectic, and you'll be that rarest of things: a nation engaging modernity on its own terms.
#4: Offend labor standards the world over. Yes, you may have coal, or oil, or unobtanium alloys. Can you extract them domestically on a modern scale? Probably not yet. Various nice foreign people will offer to help you do so. Don't accept their offers. All of them end in you being a satellite state or a colony.
There is, however, one resource that you can exploit: people. One side effect of being underdeveloped is that both your costs and standards of living will be somewhat lower; play it to the hilt. It'll bring investments and initial business in. It also primes your economy for future growth. Once your population's had a taste of what the world can offer, they're going to want it enough to fight for it.
#5: Show the world that you mean business. Pulling a Meiji doesn't require this step, but if you get this far it's probably inevitable anyways, so you might as well prepare for it. Sooner or later, to really join the club, you're gonna have a bare-knuckle brawl with an A-list nation. You'll need to win every big battle, and don't settle for anything less than a white peace.
Where possible, pick a fight that stands to bolster your economy. That coal, oil, or unobtanium from earlier? Odds are that the ancien regime gave the extraction rights to some perfidious foreign devils. Taking those rights back might be a worthy self-assertion. Racism might also help here; you can (and really should) start the war, but your opponent should go down as the one who provoked it.
This is why you did all that networking in step #3: you'll need every friend you can get, because even your allies are betting against you. Old military mentors to applaud when you show off the moves they taught you. Contacts in finance to float your economy through the darkest days. Friends in very low places, to help you win above your weight class. Drinking buddies in embassies to sour relationships with your opponent. And through it all, hordes of war correspondents to make your every triumph known to the entire planet.
You'll also need luck, but that was covered at the beginning.
#6: Profit! Step onto the world stage when your name gets called. The top tier isn't looking down their nose at you, and the bottom rungs want to be your kid sibling. Hear their whispers? the strobes popping? the crowd roaring? That's history being forgotten, and legend being born. The turmoil of the new regime, the squalor your populace endured, the dark nights of the soul as you fought a war they said you couldn't win - that's behind you forever, and nobody's going to remember that. Obscure authors will argue whether the world is your Wank.
Step onto that stage when they call your name. And when they pin that blue ribbon to your chest, remember the magic words: "I'd like to thank all my friends. I wouldn't be here today without them."
It's nothing but the truth - and nobody's going to remember that you said it.