I told my kids that waking up didn't mean the rest of the world was awake. It was quiet and sleep time. If they didn't want to go back to sleep or felt they couldn't, that was fine, but they were not to get up and they were not to wake the "house" up.
I told them they had to stay in their beds until the "house" was awake. That meant the lights were off, TV's were off, Mommy and Daddy were still asleep. The neighbors will still asleep.
Waking up wasn't the same as GETTING up when it was too early to start the day.
I would really try letting him have "rest" time during the day. Get him in the practice of laying down quietly in his bed for a certain period of time. Tell him he does NOT have to go to sleep, but he has to be quiet and let his bones rest. My kids weren't great nappers, but they had "quiet time" every day and they were expected to stay in their beds. Sometimes they konked out and actually napped.
I think if you do that during the day, you might find he'll get a little rest or at least some down time and then it helps with practice of being in his bed and quiet even if it's 4:45 in the morning.
Like I said, being awake is NOT the same as being up and going when the rest of the house is still asleep and quiet.
It worked for my kids. Give it a try.
Best wishes.