Generally a 12 week old should can still be waking for feeds during the night, and it can be completely normal for them to do so for months. Matilda still can wake up at 4am when the air gets a bit more chilly for another tuck in & maybe an extra blanket on her bed. Does the temperature drop at 4am? Do you think this could unsettle him? Even now if Matilda wakes up at that time we give her a bit of comfort & cuddle & maybe a tiny bottle if needed to help her back to sleep & most times she gets back to sleep. It was a hurdle for a while getting her to learn that 4am wasn't wake up time for good, but we treated it as if it were a midnight wake up. We leave everything dark & go in and check to see if her nappy is full, if she is warm enough & if needed give her a bit of milk to settle her back down.