Hi T.,
Here's what to do (might take a few days to get him settled):
Make sure his routine fall in this order-feeding time, then wake time, then nap time. So, he should eat and then stay awake for a bit until he seems tired. This may only be a total of an hour from the time he wakes up. Then put him to sleep but don't rock him or anything like that. Just stick him in bed and let him work it out.
He should wake up around the time of his next feeding which should be no less than 2 1/2 hours from the beginning of his last feeding - usually 3 to 3 1/2 hours from previous feeding. Then feed him, play with him, and put him back to bed.
If he is having a hard time falling asleep it may be from being awake too long and becoming overstimulated. Try reducing his wake time by about 15 minutes and see if this helps.
Most of the time the reason babies have trouble sleeping for more than a few minutes is due to reversing the order of the routine and putting the baby to sleep right after eating.
This has worked for every single baby I have ever taken care of, including both of mine (I have a 10 week old and a 10 year old).
Oh, also helpful which it seems like you have down is to have a scheduled first feeding of the day. This will help your baby's metabolism settle into healthy cycles. Try to keep it within a half hour (like between 6:30 and 7 am). If he wakes up at 5 am to eat then feed him and put him back to bed but be sure to wake him at 7 to eat and start your day.
I hope this helps!
E.