I have had some remarkable stories spin out of starting a story this way. Follow your character down a blind alley or into a mall and see where it takes you. Remember, there is no right or wrong way to tell your story. Tell it your way, especially the first draft. You can always tweak in edits and later drafts.
Use your first draft to get the story down. They you can edit and revise to your heart's content until you are happy with the finished piece... or you hit your deadline, whichever comes first. Ha!
An example: this is from a novel that is not finished yet called Blood Shot (although, that could always change between now and publication).
I needed a break from my two main characters, who we have been following for several chapters. I felt this was a great place to switch to another character, but everyone already introduced was tied up. I was stuck for what to do, but I knew there was a thief we would see later, a bit character, but important. I thought this might be a good time to introduce her.
I started writing the chapter focusing on a man, a new character who was spinning out in the writing with no real planning. I wrote a whole chapter with him, introduced the thief, showed her steal his access card, all bits that needed to happen, but I still didn't know how this guy fit the story. He felt too important a detail to simply be the way in for the thief. I liked the chapter, but didn't know if it fit. I set it aside and went back to the story points focusing on the leads.
Two chapters later, I knew not only how the guy fit in with the story, but his presence became integral to the plot and to one of the main characters. It all worked as though I had planned it out.
Sometimes it pays to follow your gut.