Although I think this is very normal, it doesn’t make it any easier for you two!
All babies are totally different and what works for one often won’t for another, and what works one day might not the next! Mine is a bit older now and has never been a great sleeper (and often terrible!) but it does mean I’ve had the opportunity to learn and try a lot!
Depending on your baby’s size, I would try getting a Grosnug (by Grobag). The “light” version would be suitable for the hot nights we’ve had (their website does a handy guide for what to wear at what temp - can be just a nappy.)
The beauty of this is that you can put arms in or out with poppers and the legs are relatively free. A sleeping bag also means you can transition from arms to basket relatively seamlessly, and it’s even safer than cellular blankets.
Then download the SoundSleeper app on your phone (its free up to 30 mins of sound - if it works the full app for unlimited play is a few quid I think). It beats YouTube because you can leave it on but still use your phone! For a lot of babies the sound needs to be louder at first than you would expect - the womb is very noisy apparently. I start mine at max phone volume.
Aim for a max awake time of 1-1.5 hours at first and let her sleep on you if needed at first. Get a great book or series on Netflix so it’s reasonably pleasant (I think this is actually quite important)
You may find you can then start to put her down using loud white noise and arms in Grosnug.
It sounds like shifts with your wife will be the best way to get through when she is able - eg you could do 7pm - 12am while she sleeps and she can take over 12am-7am while you sleep ideally elsewhere and with earplugs. At first it’s nice to muddle through together for support but if you can’t take time off you will need sleep and shifts make more sense.
I think it’s key to agree shifts in advance if you can - my DH luckily had paternity leave so would take her all morning for the first week and bring her to me for feeds. It meant that being up all night (with my kindle book!) wasn’t so bad because I knew I could sleep in the morning.
Microwave meals are fine - try to get relatively healthy ones and otherwise eat as well as you can, it will make you feel better overall. That said, if only chocolate ice cream can get you through this then go for it as well! Whatever it takes 😊
Good luck!