Overtired baby… help

Any moms experience an overtired newborn?? My baby is about to be 4 weeks and I understand having a sleeping routine is impossible so early on but he is staying awake for 4-5 hours at a time throughout the day!! I’ve heard the maximum time is 45 minutes to be awake. Now he’s at the point where he is so overtired it’s almost impossible to soothe him to sleep. Going on day 6 now. We try everything, feeding him, always has a clean diaper, doing bicycles and stretches to make sure he isn’t gassy, etc. I am now sitting with him in the dark room and he has his pacifier in with white noise in the background and it still isn’t seeming to work. He will fall asleep for about 10 minutes then wake up screaming, I feel like he might be having nightmares but hes waking himself up. Any advice?!