Is it possible to get a visa while staying in the country of China?

I'm asking this question because I plan to take a trip to Zhengzhou in early April. I have neither a passport or visa, but will purchase my passport within a few weeks at the US Embassy in Japan. From what I read, they do not issue permits for China. The reason I'm asking this question is because I'm not sure how long it'll take for my passport to arrive and if I'll still have time to get a permit for the trip. How would the process work if I come in after once I get my passport? Can they mail my permit? I'm a US citizen living in Japan. Any help would be appreciated.