I feel you OP, I feel I've spent my children's childhoods in clutter because there is no time. And I'm not a single parent either!
I would recommend videos eg Sort Your Life Out for getting in the zone and inspired.
I've taken half term off work for a head start of decluttering. It's so brilliant to finally have dedicated time. (children now adult/teen! so dont need halfterm time for child caring)
First day I just did a couple of kitchen "doom" drawers in the way people have described above. It was great practice of the principle of bin / recycle / donate / keep while keeping it not overwhelming, and being able to clear right up again quickly after sorting.
Second day I decluttered half of the "shove it there and deal with later" stuff in our bedroom. I had booked a tip visit and then went to charity shop straight after, so again I was able to get back to "normal" and the stuff left the house.
Two lessons from that day - I found stuff I had previously DECIDED to take to the charity shop, but hadn't found time. Finding time for that step is important!
Secondly I found the small collection of the most sentimental of the cuddly toys. (Previous efforts had reduced the cuddly toy stash to only a very small number, but I find this sort of sentimental thing one of the most challenging.) Some sort of moth or insect had got into the box and damaged them beyond saving. My teen was there to be consulted and showed none of my sentimentality. So these finally went to the dump.
That's a massive lesson for me. Any choice to keep stuff also means a decision to maintain / dust / clean that stuff. Otherwise, no matter how sentimental, if you donate you give someone else the chance to use that stuff before it deteriorates / breaks.
Third day I deep cleaned one of the kid's bedrooms, in this case only a handful of rubbish / decluttering as cleaning rather than tidying was the main issue.
Today is allocated to the garage pit of doom - again a dump run has been booked.
Good luck OP, I would remember that there is so much of this that is psychological issues and be aware of that and also kind to yourself. That's why these videos and resources can help, in helping you get the mindset to let go of things and promote your own wellbeing in doing that.
Secondly, time IS key. This week I'm doing is SO good but I've spent years not having the time. Think of ways you could create the time, eg someone who could take your kids out on a trip or something.