I read a sociologist once who said that’s not actually true. What typically happens is that a woman will look at a man, and then he’ll approach her. And before the women look at the men, the men do things like (this was a long time ago) display their iphones and otherwise attempt to look appealing. The sociologist referred to “lekking behavior”.
This makes intuitive sense to me, as women are frequently creeped out by unexpected male interest.