I consider an earlier Chinese space program to be a very difficult thing to achieve (only slightly easier than the Sea Mammal of lore and fable...).
First off, the Chinese human space program had a habit of coming in on the wrong side of political disputes--as your link notes, the Cultural Revolution severely disrupted this particular program, and several times the people involved were investigated for treason and such. I suppose that is probably because the leaders of the PRC at that time were not scientifically-trained and didn't care all that much about science per se.
Second, Chinese industry was at the time rather technically backwards, like Soviet industry. It would have been difficult for them to reliably produce flyable rockets and capsules. Not impossible, by any means--after all, they did construct a credible ICBM deterrence force--but it does increase the number of barriers to successful operation, and especially the expense of such a program.
Third, and probably most importantly, any Chinese program would necessarily be disproportionately expensive (due to its limited GDP until recently) and of limited benefit. Unlike the USSR or USA, China probably could not expect any major propaganda success from human spaceflight missions, and most practical needs, such as communications, earth observations, or spying, could and can be better met by robotic satellites.
Especially due to the above mentioned limitations of their industry, the actual space path the Chinese followed was very reasonable, focusing mainly on developing satellites to perform practical functions, and only later developing a human portion. Now, once they decided to develop a human portion they could have (and should have, in my opinion) developed that faster than they actually have; for instance, their last flight was two years ago. They probably could be reaping propaganda benefits now, considering that the Russians have no money and NASA has no Shuttle (well, starting next year), but their inactivity has kept that from happening. I suppose nowadays they don't really care about propaganda anyways.
If you want the PRC to develop space flight sooner, my suggestion would be to somehow preserve the alliance with Moscow longer, perhaps by removing Mao in the '50s and replacing him with someone less ideologically inclined. That would help remove the second and third barriers, and perhaps the Chinese human spaceflight program could start in the early '80s instead of the early '90s.
