Ulan Batar --> Beijing

Hello! I would like to travel from Ulan Batar to Beijing, and I see that the K23/24 is recommended. BUT I need to travel on Sunday (not Thursday), and the K4 is the only one that leaves Ulan Batar on Sunday for Beijing. Is it possible to jump on the train mid-way in Ulan Batar on Sunday to get to Beijing? Thank you!