Bunnies differ greatly in their level of security and comfort. You are doing absolutely the right thing in not pressuring him to come out. He will when he’s ready. Remember, you have years with him, so there is time to take things slowly at a good pace for him.
I would leave the exercise pen open and sit or lie down near the opening and ignore him. read a book, work on your pad or laptop, and just hang out there where he can see you. Tuck a treat or two into your pocket or closed hand. The let him slowly explore you. You will be surprised at how a few days or evenings of doing this will increase his curiosity and courage. 6 weeks is about 2 weeks too young to be separated from his mother, so he really is still in very early development. Everything is new. Even food.
A bunny will explore his environment, then return to known territory, then explore again in ever-widening circles. He will learn it’s his house too and get more comfortable in his cage and xpen as he ventures out farther.