Personally, I don't care for ambition. It's a neutral for me.

What would give me pause is having children already. In my twenties, especially early twenties, this would have been a deal-breaker. At our age, it's not a deal-breaker anymore but if I were single, I would have a strong preference for a man who does not yet have kids. Nothing against single parents, it's just that the situation makes everything harder/more complicated.

The good news is that things should get better because many people are like me: in their twenties, they view it as a deal-breaker; in their thirties, they are more open to it. So as you age, your dating pool should become more and more open to it (assuming you're looking to date women in their thirties). I don't know if you try to date single moms but you'd likely have a better chance there too.