If a man does not say yes to kids, he means no.
This. He isn't saying he does but not yet. He said no.
But then said he would have kids with you just to stay with you.
Thats a carrot dangler right there.
Classic, and adding in the we'll talk about it in a couple years/when you want to have a baby has just confirmed that one.
He won't even discuss it now.
He will keep you dangling as long as possible because you've just moved in together and his life is currently rosy, and he doesn't want that to change.
For now.
So as long as he can dangle that carrot of possibility for as long as he can get away with it, he will be a happy man.
I fully expect his answer will be the exact same in 1, 2, 3,4, 5 years time. Until you are fed of carrots and leave and he'll then be married and a father within a year, with someone else.
If he doesn't want to discuss it now, he never will.
I mean you are both a good age to start thinking about a family. You are in a commited relationship and have just moved in together. if he doesn't know now how he sees his future with you, he likely never will.
He'll be the same with marriage I expect. have you broached that one?
If he is coming at you with 'not sure' or its 'not the right time' or he 'hasn't thought about it yet' or even 'yes I want to marry you, but we'll wait a couple more years' then it sounds likely he hasn't really considered an actual future with you in it.
Don't let him sit on the fence. Tell him it needs a discussion and he needs to seriously think about it because you do not want the same conversation in 2 or 3 years time when you are ready to actually start a family.