Yes, she most likely smiled at you because she was trying to be polite.
You may have caught her on a good day.
She may have ended up smiling at several people today besides you.
You won’t know how she will respond to what you do until you do it.
You don’t have to be looking in her direction as you talk to these other girls.
In fact, you shouldn’t be.
The whole point is that you are oblivious of her and just going about your day having fun engaging in these activities and talking to other girls that you encounter.
Just be yourself and talk to these girls the way you would any other person.
With this approach, it would never come off as staged.