The thing is, it is better to show interest up front. If a guy is too shy to show interest up front and becomes friends with a woman he is attracted to, and then shows interest later, he runs the risk of giving offence - because to the woman it may appear that his friendship was not sincere but rather a sort of manipulation.
Or alternatively, if the friendship is clearly sincere, she may not wish to risk it on the uncertanties of a romantic relationship.
There are many who beat the odds, but over all, it is best for everyone to demonstrate interest up front. Most women in my experience are flattered by the attention and, if they do turn you down, will do so kindly and no harm done.
Learning how to demonstrate interest, recognize interest in others, and accept rejection with good humour are perhaps the three best skills a young man can learn, because one of the areas in which sexual inequality is still very marked is that men are still, on average, expected to make the first move (though I’ll be the first to say this is no invariable rule).