Baby fussy only at 2am

I’m 9 days postpartum with my first child and I generally have an easy baby. He wakes up for feeds every 2/3 hours which is normal. It’s just that everytime he wakes up for his 2am/3am feeds, he cannot go back to sleep and is fussy. My husband and I tried carrying him and soothing him to sleep, using his pacifier, taking him out of the room for some fresh air but nothing works so far. He usually will only fall back asleep after his next feed which is the next 2/3 hours. Is this normal and what can my husband and I do?