American Applying for X1 student visa in Kazakhstan

I am an American passport holder. Is it possible for me to apply for a Chinese X1 while I am in Kazakhstan? US citizens are allowed 30 days in Kazakhstan without having to buy a visa. Assuming I have all the relevant documents, such as the JW 202 and proof of admission from my university (as well as a current X2), can I get a Chinese entry permit at the Chinese embassy in Kazakhstan?

Thank you