Starting a life-long relationship has to start somewhere. Don't shy away from simply introducing yourself to a girl. You can't marry someone you don't know. The person may just become a good friend or she may be the one, but you never know either way until you start talking to the person and getting a good friendship going. I'll use Bono for example: he met his future wife at just 13, they married nine years later and are still married 37 years later.
Moral is: you never know who you may meet, so don't let good opportunities pass you by. However, don't just go walking up to girls on the street, that will probably scare people away.
If you see something special in the relationship, pursue it, even if it means a long-distance relationship and perhaps only seeing her once or twice a year. It is doable.
Someone has to make the first move and the other person may not be brave enough to break the ice and they will probably admire you if you are the one who does start the conversation, and be yourself, if you really want to pursue a relationship any hidden traits will surface soon enough and you don't want to go through the pain of the break-up if the person rejects you later on because of those traits. It is better to just put everything up front and let the person decide if they want to be friends at the beginning.