That is a great question and it obviously varies from case to case.
But that isn't the really important point OR, more specifically, the question should be "Should you be the first man to date a woman after a breakup?" Because you really, REALLY, don't want to be that guy. You don't want to be "rebound man" to the woman who seriously has way too much baggage and is looking to make a point with herself. And you certainly don't want to have a relationship with that person at that time.
So, the question is when is it safe to date a woman after a breakup. Gage it by the amount of time in her previous relationship and how it ended. If it was a long, bad, relationship - it's got a radioactive half life twelve days for every year it lasted and tack on another week if her best friend mentions that she still talks about her ex (in either good terms or bad).
It also depends on what kind of man you are? If you are not looking for a commitment and someone just to take to dinner and a movie - provided that it's harmless enough, you can test the water a bit. If you want to go onto "whatnot" (and heavy on the whatnot) wade into the water carefully. The last thing you need is a psychotic woman crying in your apartment all to the tune of "WHY DOESN'T HE LOVE ME ANYMORE?!!!" You can picture the leaking mascara along with the "Joker" like mask in runny makeup attached to an emotionally unstable woman.
You really don't want that.
Give her space, if you know the woman. Tread carefully. Be respectful. And leave the hanky panky for after she's gotten over her last ex.