My baby's wake up time is 6 am. If he gets up earlier (between 5 and 6) I give him a paci and rock him back to sleep. Otherwise he has a hard time getting through the day. He doesn't poop until later in the day when he has a bottle, though. (For some reason he's decided he only poops when he eats....silly boy.)
What time does your baby go to bed? Mine is almost 3 months and he goes to bed around 7:30, we give him a bottle in his sleep about 10, and then he gets up about 2 for another bottle and then is good until 6.
If you are interacting with him, turning the light on, talking to him, looking him in the eye, he's going to wake up and think that's the time to get up every day. If he poops, try to change him with as little light as possible (we have a dim Iron Man night light above the changing table) don't talk to him, just change him and put him back to bed.