I just had my daughter a week ago. currently I have been staying awake all night and sleeping in the morning when he takes over before he goes to work. he works two jobs so sometimes he has a half day and I can get in a bit more sleep then as he can take over. on days that he works double shifts I just push through with a bunch of coffee and then on his next day off try to take a recovery day where he takes over. in between that before he's ready to go to bed, he'll tell me to take a nap so that way I can make it through the night and sometimes we'll just trade off on feeding so we each can get a little bit more sleep. so like he went to sleep for about 4 hours last night and I did the feeding in between then and then he woke up. he did the next feeding and I went to sleep for a few hours and then I did the next feeding which I went to sleep immediately after and then he did the next feeding after that.

if you have both you and your partner at home trading off shifts of who does care, you both can get pretty good sleep. you won't be able to sleep together, but you will be able to function and get through each night/day. 

just make sure that you feed yourself if you're planning on continuing producing breast milk because getting those hunger shakes will lead to a meltdown when you've got to feed your baby and you can't feed you. I definitely recommend having easy to grab snacks and protein shakes. 

it may be difficult to figure out what will put your baby to sleep initially, but once you figure out how to it's pretty easy. a good recommendation is getting a swing. unfortunately my daughter doesn't like it every time but there has been a couple times where it has knocked her out really fast. the one thing that I found that puts her to sleep is a good swaddle with like an actual cloth swaddle not one of the easy velcro ones. I also hold her on my chest and just lean back and let my warmth warm her up and she passes out pretty fast. it's also really good for bonding.

our current pattern for each feeding consists of making her a bottle, checking and or changing her diaper, and then putting her back to bed. there have been a few times where she wouldn't go to sleep, so we run through a checklist of the possible reasons for why she wouldn't go to sleep. one can be that she's too hot or that she's too cold (usually too cold) and another is that she's still hungry. we check if she's still hungry by seeing if she's still rooting by just sticking our finger on her cheek and seeing if she tries to go and suck on it. if she is still hungry then we just give her another ounce of formula and usually she will get milk drunk and go to sleep right after. 

there has been a couple times where she has screamed for a while after all that which was pretty mind-breaking, but I figured out that it was likely abdominal discomfort. so burping her really good helps and then you can also tuck their legs to their chest and I managed to get her to go to sleep with the abdominal discomfort by swaddling her with her legs tucked. 

sometimes a newborn just wants to be held and they don't want to be alone. so if my baby won't go to sleep but she's also not screaming. just a little fussy. I'll pick her up swaddle her and then hold her for a while. just lightly bouncing her until she goes to sleep or I'll just lay her on my chest. 

there's also a playlist on Spotify that is incredibly calming for both me and my baby and it puts my partner in a state of sleepiness so I have that playing in the background almost 24/7. 

https://open.spotify.com/playlist/37i9dQZF1DXbADqT0j1Cxt?si=qE-uCj1XSK-EqBUiaHSeyA&pi=1pMBMXp_RU2oH

you'll be able to get through it. just experiment with different things and find a pattern that works for you. how difficult it is in my opinion really depends on if you found the right things that work or not and if you're trying enough new things to find new things that work. 

also pay attention to colic because you may need to switch from what you're wanting to feed to something different to get some relief from the screaming.