Can I book train tickets on the day?

Hi, all of us (4 adults & 2 little kids) will travel to China during the 2nd week of December and move from Shenzhen railway Station To Guangzhou East station and from Guangzhou East to Hung Hom station. Do we need to buy the tickets 1-2 days before or it is possible to buy the tickets on the day so that we do not need in a rush to get to the station?
Thank you