Of course, you can. But the train tickets are usually started being sold around 10 days before departure. And you would better buy it in advance in case there are no tickets left when you buy on your departure date.

It’s very difficult to buy train tickets on the same day of your preferred departure that is based on what we have experienced. Our itinerary was Shanghai-Beijing. We got D32 ticket and it's neat and comfortable. But going back to Shanghai we got T-Train ticket-trains are not comfortable, very crowded and the lavatories are dirty. I suggest you to buy in advance or you can reserve first class ticket from travel china guide for your convenience.