More land area (i.e. standard or larger map size, and pangaea or continents) could improve the relative value of China vs. the other civilizations.
This is because the Chinese rider has more movement points than a knight.
Also China is militaristic, which means: more elite promotions, more great leaders, and more armies.
Armies get an extra movement point - your rider armies will move 4 squares per turn.
You can try setting barbarians to restless or raging, they will help promote your horsemen to elite status and accumulate cash for upgrading them to riders.
You will have to learn how to deal with the barbarian uprising that happens when you enter the middle ages. For that purpose, I build spearmen in the late ancient age to defend my territory. Even at warlord level your elite horsemen can't survive a barbarian horde, but most of your spearmen will.
To get armies you will need to have elite units defeat another civilization's unit (not a barbarian unit). You can declare war against someone - or refuse their demand - and use your horsemen to pick off the warriors, archers & horsemen they send into your territory. Your horsemen will be too valuable (think "future rider") to risk against enemy spearmen or swordsmen, so you will need a few swordsmen yourself.
You should make it a priority to build the heroic epic; it improves the chances of getting a leader. The heroic epic requires a victorious army battle, so your first army will be an army of horses or swords, and all the rest of your armies will be riders, until you get cavalry.