I was having a similar problem with my bunny, and I don’t have a real bedroom to shut her out of at night. Here are some suggestions:
-buy earplugs, lots of them, for yourself. Try different brands to see which fit you best for comfort and noise cancelling. TBH that’s my best suggestion.
-attach an xpen to his cage, like Mikey said, so that he can exercise at dawn without disturbing you (not a great solution, if your bunny likes to rattle xpens, too. Mine does)
-make it a priority to be sure your bun gets as much exercise as he wants before bedtime
-when you have destroyable toys like willow balls for your bunny, put them in right before bedtime, so that when he is feeling rowdy in the morning, he will have something to do
-try feeding pellet ration at night, so that he has something extra to munch on while you go to sleep
-wait it out. My bunny has gotten a lot quieter first thing in the morning. I’m not sure if she is adjusting to my lifestyle, or if the changing seasons is making her sleep later, if she’s grown tired of rattling her pen, or what, but she has been much quieter lately than when I first brought her home. Or I am better at sleeping.
I hope something on that list helps you out! (but seriously, try the earplugs, you want those!)