He is still very young and I think its just a case of giving him time and catching up on sleep while he sleeps if you can.
I'd not be inclined to start trying to keep him up as all you'll get is a tired miserable baby. And you'll want his sleep time to get earlier as he gets older, not later so I'd say stick with him going to bed then if he is tired.
You could try a dreamfeed around 11pm is the only thing I can suggest. I used to dreamfeed LO on occasion but tbh I think it used to make him more hungry and he'd still wake a few times in the night. But then he is breastfed and thay digest quicker. By about 12 weeks is when you can expect baby to be able to sleep thorugh without possibly needing a feed at some point. Many formula fed babies sleep through sooner, but not all.
I started cluster feeding around 14 weeks and he's been brilliant at sleeping ever since. The odd night when he wakes at 4am or so but mostly goes through from 8pm to 6am. It can work but its not for all babies. Some just won't do it. And it takes a little while to get baby to adjust to taking in the extra ounces. Maybe more so with formula fed babies as its thicker and more filling than breastmilk. And takes longer to digest.
Also don't forget the growth spurt stages. One around 7 weeks or so might mean he is waking hungry in the night.
You could also try to not feed him and give him a chance to settle himself again, maybe turn the mobile on or whatever you do that settles him. Make feeding a last resort not a first one.