I am now in the Mugunghwa train bound for Dongdaegu. I will get off at Suwon station and it’s estimated to take around 30 minutes.
I bought this ticket online but you can always buy on the day itself. I just want everything covered just in case.
Also, Suwon is connected to the Seoul subway system. However, that takes around an hour if you’re coming from Myeongdong.