Men develop a power of action and women develop a power of attraction.
I talk in average, ask men how many times a woman they like went to them, and you will be surprised, it's very rare.
Unfortunately, if a man wants to have a chance, in 99% of the cases, he has to go to the girl if she is unknown, a little less if she is known.
It's not only the first step : every new step (risky move) of the relation is initiated by the man : go talk to the girl, propose to do something with her, the first kiss, take her hand, etc... The woman on the contrary, refuses, accepts or slows down the attempts of the man.
And its consistent with biology, ethology and anthropology: males fight each other and their own limitations (timidity, fear, stupidity...) to be strong for the female they want, it's the best way to select the alpha male (the dominant one) who will transmit his genes.
Men have to know this if they don't want to ruin their sentimental lives waiting the girl of their dreams go talk to them. And similarly, women also have to know that they have to be attractive to activate the interest of the man, even in the relationship.
Here is an interesting article with statistics on the subject of the first step.