It's all too easy to over complicate matters that's because for many of us we tend to over analyze. As they say analysis can lead to paralysis and as a result we do nothing. When approaching any woman anywhere just be sensitive to her situation.
Don't just invade her space and expect to be greeted with open arms. With that said some women may just be having a bad day and you come along at the wrong time. If this happens and you have a bad experience for goodness sake don't let that one experience dictate everything you do for the rest of your life.
Frankly it's all about creating opportunities. People who create opportunities set themselves up for success and those who judge everything set themselves up for a miserable life.
A simple smile is a gesture that is inviting and if a woman takes you up on it the least you can do is say "hi". Then just make general conversation about what's going on around you and do not get personal.
At a later stage when the conversation is underway you can introduce yourself and she will naturally oblige by giving you her name and then you can take it from there. Always monitor her body language and adjust based on the reception you get but never over commit yourself this way you do not burn any bridges.
To conclude, Yes - a simple smile and being a happy human being has this magical ability to create opportunities.
Guy's if you are serious about getting the girl of your dreams then you need to seriously work on solid techniques to achieve your goal. If you know what a girl is thinking it is far easier to approach her.