OP, I feel you. My H left me and literally took away the life I envisioned for the future. It took me to rock bottom.
Very similar to you, I found i just initially didn't have the time to go on dates, if the kids ever stopped out at my parents it was because I was working at 6am the next morning, and I didn't want to be seen to be taking the piss with childcare with them just so I could go on a date.
I also found married/coupled up friends are wary of inviting a solo female to group things? As though you might suddenly run off with one of their partners? It was very odd to realise that so many of my friends regarded me as a threat once I was single
As previous posters have said, you need to try and build a little network. Don't do OLD, it's a cess pool. But try and do little things that build your network, I started going for a little walk on my day off, and you see the same people, and start saying 'morning' then you see someone with a limp or whatever so instead of 'morning' you ask if they're ok. It might not seem like much, but little steps build a framework.
Also I've reconnected with some of my cousins, which is lovely as we'd all lost each other in the 'children' years
I appreciate that if your kids are small and you have them full time you literally cannot get out and socialise, but if you have hobbies there are 1000s of online groups sharing info and ideas, I'm a member and lurker of various groups including needlework, motorbikes, cats and old cars.
You're in the trenches now, but it will get better xx
I'm just editing to add, I've tried all of the above, and it's worked in terms of meeting people
However, do not jump into a relationship with anyone unless everything is perfect. Look after yourself