You learn to live on less sleep and more coffee. It'll get easier.

Congrats, OP! Yes, it is absolutely brutal, and layering a new job on top of baby is doubly so. I returned to my "old" job after #1 was born, but started a new role (same co) after #2. That kicked off the most intense 12-18 mos of my life.
-I found (and still find, even now) that it really helps to fully connect with whatever you are doing at the moment... so if I'm at work I am AT WORK and if I'm at home with the kids I'm NOT WORKING. I do not check email or respond to any but the most critical calls while my kids are awake. Must be a division head or someone texting me that something literally expoded, or something like that.
-simplify as much as possible. Meals schmeals. Oatmeal and fruit is a lovely dinner. Pick up a ready made meal when you're at the grocery. Scrambled eggs. Whatever gets you though. I bought lunch a lot during this period, because I simply could not deal with one more thing to DO in the evenings.
-Do whatever gets you the most sleep. Lots of people will pressure you to sleep train, but committing to sleep training kind of requires some focused attention, which I know I was completely incapable of, during that super sleep deprived period. Nap when the baby naps on the weekends. The hell with vacuuming. Go to bed as early as possible, even if it feels a little ridiculous. I would occasionally go to bed as soon as the kids did, on the weekends. It felt silly but so, so good.
-Make sure DH is pulling his weight. Sounds like he is, but just sayin
-simplify your weekends. Amazon Prime will deliver just about anything. Say NO to invitations that don't fill you with joy. Take a nap. Etc.
-I wouldn't push for WFH, esp so soon into a new job, but once you have a few vacation days saved up, take one on occasion as a mental health day. Get a haircut, take a nap, eat a vegetable, take a nap, clean your shower, take a nap, you get the idea. Even just leaving work an hour early can feel really good.
-Enjoy peeing at work. You might not be at that point yet, but someday that cute little baby will follow you into the bathroom ALL WEEKEND LONG and you'll look forward to washing your hair and peeing alone, on Monday morning

Totally normal. I found that life seemed to get a little easier when each of my babies turned one (my youngest is nearly two now).

Between breastfeeding and illnesses and night wake ups and the emotions associated with leaving your baby--it's just a very challenging time.

I agree with a PP to consider sleep training (Ferber), and also I don't know if you're pumping, but supplementing and cutting back on pumping can be a relief as well.

Simple meals, go to bed early. Some times I have ended up in bed as soon as my children are, like, 8 pm. Especially if you feel like an illness is coming on.

Once your baby starts walking and talking and you get down to one long afternoon nap--I found it just all comes together better then. Do fun activities in the morning, do chores or something for yourself during nap time, another round at the playground, early dinner and bed time, then another window of time in which you can do something.

Hang in there until then.

I did not have a new job when I had an infant but I was exhausted all the time. Working with a baby at home is hard. Doing anything with a baby at home is hard. Babies are hard.

How's the baby sleeping? If she's waking up a lot at night what about sleep training her? Where's daycare in relation to work and home? My main advice is simplify everything. Meals made in advance so there's minimal weeknight cooking. Grocery delivery, get babysitters when you need a break. Shower with the baby so you only do one bath time. Etc...

Of course you're exhausted! It will get better with time, but assuming you're also 6 months postpartum, make sure you're taking vitamins. Around that time after having my son my iron levels were low and that contributed to how exhausted I felt. B and D vitamins might also help.

Hire a babysitter on weekends so you can catch on sleep.

A baby and a new job are two big things to adjust to, especially at the same time, OP - it will get better! You'll get into a groove at work and baby will get bigger and start sleeping more. In the meantime, are there things you can outsource so there's less you have to do when you get home? Have groceries delivered, that kind of thing? Might help you get some more sleep on the weekends.

That sounds brutally normal, especially for starting a new job. Hats off to you.

Can you nap during lunch?

Agree that it is normal. I found that eventually I needed less sleep. At the mid afternoon mark when I thought I would die if I didn't sleep, I always planned a break for a short walk or a cup of coffee. As to WFH, that depends on your job, but I never found it to be so great. I found it harder to work when I was tired. Much easier to be in the office with people around.

OP here - if one of us is up late the night before, the other one steps in the next morning but I'll suggest the switch schedule as well!

As for the WFH - I don't know how to approach such a conversation. I don't want to seem like I'm asking for too much being so new to the job. I technically haven't even passed the trial period which is in another 3 months. My company has been great about letting parents come in late/leave early or take a day with sick kids or late school openings though. When you say 'once in a while' is that something you would ask for as needed, maybe every couple of weeks or 1-2 month?

Thank you!

Totally normal. Starting a new job is HARD, and having an infant at home only makes it harder. Do you and your dh switch off on weekend mornings so one of you can sleep in? That might help a little. Can you do a WFH day once in awhile just to take the edge off?

I've been at my new full-time job for 3 months now. I love my work, I love the company, and I really feel challenged by what I do. It's my dream job really. But I also have a six-month old at home now and I'm just flat out exhausted every single day of the week. It could be 9PM on a Sunday and my eyes are dragging in a way that I never ever experienced before.

I have daily daycare during the week and my DH at night. It's just the sheer amount of attention and focus that an infant draws when before I felt like I had a 'normal' balance of sleep cycle and work-life. When I get home now it doesn't feel like the 'work' stops if that makes sense. I'm not complaining, just trying to give you an idea of where I'm coming from.

Will it just take time to re-adjust to this new life? Will I eventually need less sleep? Do you feel like you're dying right around 3:30pm - 4:00pm at work as well only to get off and do more when you walk through the door?