You should let him decide.
Even if you were to make a move and get his contact info, that wouldn’t change the fact that he is may still be dealing with the emotional repercussions of his previous breakup.
He would most likely continue with this kind of behavior, thereby making you that much more confused and frustrated.
If you let him decide, this may indicate that he is now serious about moving forward and leaving his past relationship issues behind him.
This would be the better way to proceed with him.
If he has claimed that he wants kids, you should take him at his word.
Operating on the assumption that he is not being truthful about that would be a major risk.
If you are wondering whether it would even be worth it to start something with this guy being that he wants kids and you don’t, it may be worth your time to pay attention to what he tells you during conversation.
If he keeps talking about kids or having a family without any prompting, there is a good chance that he does want kids.
In this case, it may be best not to pursue a relationship with him.
Try to avoid making the mistake of thinking that he will change his mind at some point as long as you talk to him long enough and he likes you.
This outcome rarely happens.