5 week old awake all night-help!

RA1109

My 5 week old wakes up atnywhere from 1am-3am and is wide awake the rest of the night. He's not fussy, just awake, chatting away. He does get fussy because he wants to be entertained, but for the most part he's just awake. It's by far his most awake time of the day, and he doesn't go to bed till 9am or later.

 

This clearly doesn't work with a toddler who wakes up at 7:30 and is ready for the day. Nothing I do gets him tired and trying to keep him up during the day doesn't help, in fact he's awake almost the whole day too, just cat naps for 15 minutes at a time. Am I doomed till 6 months when I can do sleep training?