No, it's really hard at that age. IME 4 months is a really tricky age, they are very grizzly and want holding a lot. You often get snippets of about 2-10 (maybe 20??) mins in which to do anything at all, including preparing food for everyone, going to the toilet, paying attention to your toddler, sitting in peace with a cup of tea etc.
What has helped me is having a sort of "layers of cleaning hierarchy" - I used to have this as Kitchen > Bathrooms > Living room > Hallways > Bedrooms. But even that was a bit too in depth and I would always feel like everything was chaotic.
What I have now is this idea:
Dishes > Bins > Kitchen floor (JUST clutter) > Laundry > Kitchen sides wipe down > Bathroom floor (JUST clutter) > General tidy (toys etc) + hoover > Anything else that looks visibly dirty (bedding change, bathroom sink/toilet, floor mop, etc)
What that means is that on any given day is that the further forward on the left something is, it's more important that it happens. If the dishes get done and literally nothing else does, that's absolutely fine. Most days I get about up to the bathroom floor, on a good day I get further, some days I literally load half the dishwasher and that's it (and that's FINE.)
When DH gets home from work he generally does dishes/kitchen counters and just before the DC go to bed he leads a "tidy up dance party" (more energy than me!!) unless they are totally exhausted, and then whoever is not doing bed/bath will tidy or finish up tidying the front room and then we have one of those robot vacuums that we run after they have gone to bed. I can also chuck this in the kitchen during the day which is why just taking "stuff" off the kitchen floor is the priority. Reduce toys down to a manageable level too and store with like things - so all farm animals together, all play food together, all toy cars together. Makes it easier to tidy up and easier for them to get the one specific thing they want out, not dump every box out looking for one thing. Some people do toy rotations - I can't be bothered with this, but I do weed out old/outgrown/broken/incomplete toys quite regularly.
Disclaimer I do have a handy teenager to take down the bins as otherwise this would be a particular sticking point, as we live in a flat. When I lived in the house, it was a bit easier as I could just open the back door and reach the outside bin from there. If I did not have the teenager this would also be DH's job as soon as he arrived home before he took his shoes off - because it's a huge pain to do this with a baby and toddler.
All this in practice means that the bathroom gets cleaned less than it should, but I just don't worry that much about it.
So if I get a moment in the day I will empty/fill the dishwasher, bring plates from other parts of the house, scrape food into bin, however much of this I can get done in the 2 mins that I have or whatever. Then once that's done, check bins for any that are more than about 80% full and empty, then check for what laundry needs moving over, putting away, starting etc.
Dishes are the most important because they clog everything else up if they get left behind, the left out food smells and is dangerous (breeding bacteria etc) as well as making it hard to complete basic tasks like making food. Having a dishwasher makes a massive difference because it means that you can just do 5 mins at a time whereas having to hand wash means running water and then doing as much as you can before the water goes cold, which is a pain.
It can be tricky to empty the dishwasher with a 2yo but at nearly 3 perhaps you can give her jobs - pass her all the plastic stuff, a cloth to dry them off, and a basket to put them in, then transfer the basket to a counter/cupboard when she's done (lots of praise). Hand her the cutlery basket, with knives removed, and let her put them away in the drawer standing on a chair. If you have one of those newer dishwashers with the cutlery tray thing, see if you can buy a basket for it for now just for this purpose.
Bins similar - if they're full it prevents things from being thrown away so all the mess starts to expand extremely rapidly.
We bought a tumble dryer. I was spending so much time on hanging hundreds of tiny items up and this has saved my sanity and freed up so much time.
Also, partially done laundry is ALWAYS in a laundry basket. This prevents it from spreading around and getting mixed up with dirty stuff and then you have to wash it again because you can't tell what's what. Having every task being interruptible is key with DC of this age.
Will your nearly 3yo start preschool in January? That will help a bit although you'll have a 6mo then
However IME it's sooooooo much easier once they can sit up, as it means that you can plonk them next to you for 10 mins or so while you do a job. Hand them a clean saucepan and wooden spoon from dishwasher while you empty it, taking sharp/breakable things out first. Hand them a basket of unpaired socks while you sort laundry. Let them play with dryer balls. Get them to "help" you put things into/out of the machines, let them put the tablet or washing liquid in (very well supervised). Move them to each room as you put the clothes away etc.
If I had to rate household appliances for essentialness when DC are little:
Washing machine
Microwave
Dishwasher
Some kind of quick hoover (hand held or robot)
Tumble dryer