Sorry that things are tough for you, OP.
One thing I can hopefully reassure you of - I found myself single in my mid 40s and had no problems at all meeting men, many of them perfectly nice and also attractive! And I have quite a few female friends same age or even older in the same boat, and again it not been difficult. Most of them have met people through internet dating, one met someone through her work, one through the gym..... Most of us are moms and have dated mainly single dads, tho actually my now husband is child free by choice, yet gets on well with my daughter......
As your children get older they will have playdates and sleep overs, maybe do some evening clubs - it WILL be possible to date if you want to, as long as your dating partners are happy to be flexible. You may also make friends with parents who are happy to babysit for you sometimes if you return the favour....
I'm obviously not saying it will be easy, and I am very sorry you find yourself in this difficult position. But don't give up hope - it's amazing how different things look as your kids start to get older.....
Also (and I may get flamed for this) - there are VERY strict beliefs prevalent on here, in my opinion, about how soon it's ok to introduce kids to new partners - and I almost feel there is an element of misogyny/slut shaming to some of it (not from all people who say it of course, but from some). The idea that a woman, once she becomes a mother, must be willing to sacrifice every aspect of her own happiness and well-being, especially if that happiness and well-being relate to her sex and romantic drive, to her children's needs......
If you are having a different bloke move in every week and forcing your child to call him daddy, of course that's wrong. If you let your children know in an age appropriate way that you are dating, and what that means, and take your kids out to dinner with a guy and his kids, say, after you have known him a couple of months, then he comes round after your kids have gone to bed once a week and you have a glass of wine and watch a movie......
THAT'S NOT GOING TO HURT THEM!
(I was dating my now husband for a year before my daughter met him. Looking back, that was a bonkers timescale - she knew what dating was and knew he existed - she is perfectly sane and was unlikely to start believing him to be her new father - I honestly don't know what I was thinking......)