Chuseok train from Busan to Seoul

Hi everyone, I have a question about how impossible it really is to get train tickets around the Chuseok holidays. I'm on a trip with 5 friends in South Korea next month and our flight home is on the 25th September. The problem is that we are in Busan and need to get to Incheon Airport on that day. I already asked Gemini and Chatgpt and one said it's impossible and the other said its possible. Is it really that brutal to get Tickets on these days? We wouldn't care if we have to take a train on tge 24th in the evening or really early in the morning of 25th. We just want to get into any train possible.