Yoo Joonghyuk's careful optimism for "This regression will be better than the last" is shown as early on as his first meeting with Kim Dokja.
For all intents and purposes, Yoo Joonghyuk had just left a regression that utterly destroyed him. His wife and child died. He was betrayed by the one person he thought understood him the most (Anna Croft, because she was the closest thing he had to someone who understood regressions as well as her vision for the End of this story lining up with something Yoo Joonghyuk wanted as well). He lost all of his companions (iirc).
He came into the 3rd regression with the determination to do everything alone. He didn't want to trust anyone. He certainly wasn't going to trust someone who claimed to see the future.
But enter Kim Dokja, who had drastically changed the timeline in a way he had never seen before. Kim Dokja, who had never been present in the story. Kim Dokja, who somehow knew him and dared to be cheeky with him upon first meeting, telling him things that nobody should know.
Putting aside the possibility of forgotten memories influencing him, Yoo Joonghyuk had every reason to dislike Kim Dokja from the start. Instead, he chose to test him. And with that test, he actually hoped that Kim Dokja's words were true.
Yoo Joonghyuk is an optimist. I think that's part of the reason why Kim Dokja could never stop reading his story. One of the reasons Yoo Joonghyuk continued to fail so much was because he held out so much hope that "this regression will be better than the last". And yes, Kim Dokja knows that didn't work out for him. But we can see even in Yoo Joonghyuk final, wretched state (1863rd regression), he still held out to a bit of hope. His little desire to not want to die yet. That little desire that wanted to truly reach the end and see the story that Kim Dokja was creating.
Yoo Joonghyuk held so much hope. And for Kim Dokja who saw no reason to love humanity, I think that's the sole reason Kim Dokja turned out as well as he did. I think that if he didn't have the optimistic Yoo Joonghyuk as his father figure, his brother, his best friend, Kim Dokja would have turned into a very dark person. And we see bits of that nihilism shine through at points in the story as well.
Kim Dokja is the guiding star of the Kim Dokja Company. Yoo Joonghyuk had been keeping his eyes on that star for a long time, even if he didn't completely remember it. And in turn, Kim Dokja had been watching him too.