Most Helpful Guy
Firstly, if you can do a police check on the man then do that first. I have come across a number of cases where a woman with a child or children has introduced the man to the kids and he turns out to have been abusive in previous relationships or has paedophilic tendencies.
Secondly, I would wait at least six months to be sure the relationship is going somewhere. You don't want to introduce someone to your kids early only for the relationship to broke up and he disappears from the kids lives - that could be very distressing for them, especially if they take a liking to them.
Most Helpful Girl
When you feel comfortable enough with the idea of him meeting them, and you feel the relationship will be long term