I can try offering input. I'm 48 but been dating for the past 3 years and also have 3 kids.
The dating market is heavily skewed towards females these days so it's easy for girls but hard for guys.
Work on bettering yourself looks wise(work out, new clothes, haircut, grooming, etc) so that you are the most marketable.
IMPORTANT: This took me awhile to adjust my thinking but GET OUT of the RELATIONSHIP mode and get into dating mode. For guys that's been in LTR or marriages, sometimes we tend to linger in relationship mode. This will easily kill off any dating prospects.
Don't invest too much and too soon. In marriages, it's easy and expected to go all in but you can't do this when dating.
Since you're just getting out of a marriage, concentrate on just meeting women, learning, experiencing, and having fun. Do NOT get hung up on a relationship yet.
Women say whatever to fit their needs and get what they want. Do NOT try to white knight and be the good guy. That doesn't mean not to be a gentleman but don't go overboard to accomodate THEIR needs. You do do and concentrate on what you're needs are and try to meet them.
Don't concentrate on securing someone or getting sex. Just work on getting familiar with women again and interacting with them.
Don't overshare info when unnecessary. For example, don't tell someone that you are still going through a divorce. They don't need to know that if it's never going to go beyond a first date. Plus divorces can take over a year to be finalized and not everyone realizes or understands that.
Sometimes advertising kids freely can work against you. I would only volunteer this info when asked or if you know they have kids already.
There's a bad rep associated with single mothers but if you're a single father, that can actually help you in some regards if you do meet single mothers.
Lastly, establish with your ex some ground rules for dating and not having the kids get involved in that in any way until things become serious.
Good luck with the divorce.