There are three ways I generally start writing a new story. Most often I start with the scrap of an idea, almost as often with a character, and once in a while a setting grabs me and starts the ball rolling.
There is a fourth way to get a story started, and it's one I've largely ignored. That method is to begin with a theme in mind. I've avoided this method of story creation largely to avoid writing fiction with a "message". I write to entertain, not educate and having my writing come across as a sermon does not appeal to me.
In researching theme and how best to use it I came across some interesting takes on theme that made me think differently. I now believe that starting with the theme in mind does not have to lead to preachy fiction at all. I also believe that the sooner you have a handle on your theme the faster and easier your writing will be.
Check out Know Your Theme and see how redefining theme can help your writing.