Also by hobby I mean reading a new book, watching YT videos and leaning a new skill. This keeps your mind simulated while not crashing out. Your baby is still very small so at this stage you have the opportunity to sleep with baby, and still do something for you. Good luck
Congratulations on your baby! It sounds like you need to create a schedule that works for both you and dad. Since he works overnight he’ll be sleep during the day and for some moms that may be frustrating considering you may need help with the baby. Then when he gets up it’s back to work. Find a in between time that work a for you both. And also, start a new hobby. It’ll keep you entertained while being with baby.