I'm not saying it will be easy, just that due to potential manpower and economy size it may be the only country where a WC is even *possible*. No other country in game can hope to have even a fraction of China's size. But the first 50 years of a China playthrough will likely be difficult.
A few quibbles :
1. We don't know how easy it will be to keep intellectuals satisfied, and due to the size of your country, you can maintain more Universities then anyone else while keeping intellectuals as a percentage of your population quite small. So the intellectual faction might not end up being especially influential.
2. While you're right about china's population in our timeline, the same is unlikely to be true with a player lead China. Indeed if a player chose to pursue policies that increased birthrates while avoiding the civil wars that happened historically, you could very easily see a scenario where China doubles or triples its population, as happened in Russia during the same period. Your population advantage could get even bigger, with China having almost half the global population, even more so if you acquire neighbouring uncivilised countries. With the size of your population, migration should render controlling such regions to be much easier.
1. Most of your population is poor farmers. They are not even politically active (until later when tech spread can activate powerful ideologies that could be destablizing) in 1836. Your IGs will be the Armed Forces, the Landowners, and if you pursue the Universities, the Intelligencia. It's not 3% of your Pops that would problem you, it is like a third of your Interest Groups that's the problem I speak of.
2. Growing your population faster than what China historically went through can only be done through 3 methods, increase the birth rate and decrease the mortality rate and massive immigration. The former is pretty maxed out in pre-industrial societies. You can do plenty of moves to
maintain the birth rate as you industrialize but you can't really increase it more than it already is in 1836.
3. To decrease the mortality rate means better technology, it means more industrialization, it means more social systems and more Institutions and more Laws, and smarter Pops and richer Pops and more political Pops. It means an increasing variety of Interest Groups. You just opened the Pandora's box you were trying to not open.
4. Immigration on a scale that actually matters to China would still mean making it an attractive place to move to. That means liberalization of the society, more freedoms and more rights, less concentration of political power, less autocracy, more industrial goods access, more education, etc, etc. You still get the same problems as decreasing the mortality rate gives you.
I really doubt that the population advantage will be greater than it was in history WITHOUT also giving up the advantages that you need for a world conquest run.