baby waking TOO EARLY! help!

Our baby is 3 months old and EBF and he normally goes to bed around 8pm. He wakes to eat at 1am, and falls back asleep. However, come 3:30 am he is up and ready for the day - screaming (happy), talking, cooing, etc. He's not hungry as I offer my breast every morning. I know he's still tired because after 30 mins or so, he begins rubbing his eyes and yawning. He normally will take a short nap around 6-7am. How can I help him sleep longer, I know babies this age need a lot of sleep!