There is an alternative meaning. Instead of expressing that "she is shy at first but eventually is less shy", the speaker might be beginning a list of things. "To begin with" can be a signal for a list, which suggests that it is the first and most important item on the list.
Example:
If you asked me why I am tired, I might reply:
"To begin with, I haven't gotten a good night sleep in a while. But I'm also very busy at work and need a vacation."
In that exchange, "to begin with" is not temporal. It is just a signal phrase, emphasizing relative importance.
