There is some good info in Mom's House, Dad's House.
One way to do it is to bump into each other at the grocery store or co-op. Or dog walking. Then you can do a casual introduction.
Then if you want to do more, you would invite him to something fairly short. No PDA. And slowly build.
I don't personally have objections to people dating before the divorce is final, but really 10 months is not that long.
If the divorce is close, why not wait and then nobody...