Bless you, you’re right in the thick of it right now. It will get easier.
I became a single mum when my twins were 4 months old, and stayed that way until they were 6 years that old. Family all dead except a sister who lives in another country. I didn’t have a lie in for about 4.5 years. My DTs did not sleep through until they started school. It damn near broke me, so I really sympathise.
I’m not giving you my story to make you feel you’ve got it easier, but to paint the picture for some tips that helped me - because if I could implement them, you can too.
The main one is go to bed early whenever you get the chance. You’re not going to get lie ins and actually they may make you feel worse because they throw out your body clock. Just accept get up time
is get up time (in my case somewhere between 5 and 6) and catch up on sleep at other times. At least once a week I went to bed immediately after putting down the twins. Sometimes we sabotage ourselves by watching TV, or going on the internet because we feel so cheated of me time we feel we’re going to lose out on child-free time if we go to bed - but me time is meaningless if you’re too tired to enjoy it. Sleep is more important.
Eat well and take regular exercise. Underlying fitness has a huge influence over energy and our ability to cope with pressure.
Maximise time-saving opportunities. If cooking spaghetti bolognese, make several meals worth and freeze them. Do this as much as possible when you cook. Means when you’re tired you can just microwave it and catch up on some rest or relaxation while still eating well and avoiding crap food that leaves you feeling even more tired.
Make sure DH is pulling his weight in terms of housework. As it was just me Ian’s the DTs this was easy for me - the only mess was what I made or allowed. Had I had to tidy up after another adult I’d have lost my shit completely.
Insist on a few hours for yourself to do something you enjoy - if it’s something that makes you feel fulfilled so much the better. Mine was running, so once or twice a week I’d ask a friend to be in the house after I’d put the DTs to bed so I could run. Only 45 minutes but saved my sanity. The rest of the time when I didn’t have a sitter, I’d skip with a rope in the kitchen. Point was it was for me - not the DC or another adult, just me. Could be painting, walking, karate, flower arranging -anything that makes you feel like a person in your own right, not ‘just’ a mother or wife.
Make sure you have a safe space to leave them where you know they can’t harm themselves and let them get on with it. I had a giant wooden playpen that practically filled my living room. When it all got too much I’d pop them in there and go into the kitchen for a cup of tea and 10 mins peace and quiet. Children won’t die from boredom or frustration at not having their every need met instantly. This helped me massively. You don’t need to be a perfect mum just a good mum most of the time and a pretty mediocre one the rest. As long as you’re not neglectful or abusive it’s fine and your DC will likely build more resilience as a result of learning to self entertain.
Lastly - keep telling yourself it’s only temporary. I know it doesn’t feel like it now but you’ll be surprised how quickly this becomes the past. Hang on in there.