You had enough sensible answers here to make up your mind, ut in any case here it goes my experience.
Normally, when I have been hitting on a girl who has just broken up with an ex, I could invite her to go out and fuck her same day-night. But if they are hurt, chances are our relationship would be a sporadical one of talking and sex, nothing more.
Other scenario has been when I have met and become friendly (but no sex) with a woman who is getting tired of her current relationship, in those cases, when they finally break up in their relationship, first person they think of is me
and I have had great meaningful relationships with them with no waiting time.
Corolary, you like her, hit on her hard and see what happens, chances are you get to fuck her and a slimmer chance is that you find yourselves in a relationship. We men have to try, always! that is the law