Do not run away from the facts; do not fill them with so many meanings, symbols, sermons and warnings. Live them without allegories. Live them with a receptive mind from moment to moment. - Samael Aun Weor
First, do not read too much symbolic significance into events in the physical world. Try to see things just as they are.
Second, Karma is a very complicated thing. It's quite possible that you have some sort of karmic connection to this girl, but not enough of the karmic causes to foster a relationship (romantic or otherwise) are present in your life.
All of the necessary causes for an effect must be present in order for that effect to manifest. So it is possible for some types of karma to remain (temporarily) unresolved if the facilitating factors that would allow that karma to play out are not present.
Just trust that if it's necessary for you to meet this girl again, then it will happen, and you will not be able to avoid it.
Also be aware that not all karmic connections have positive outcomes. There could be a lot of suffering trapped within your karma with that person that would be released if you were to meet again. Not everything we desire is good for us (in fact, most of it only causes more suffering). So do not covet that circumstance. Perhaps your Inner God is protecting you from a negative relationship so that you can dedicate yourself to the Path, or is withholding that relationship from you until a time when you are properly prepared to enter into it.
So you don't need a time machine, and you don't need to fret over a "missed opportunity" 11 years ago. Just live in the present, and accept what the universe gives to you. "Seek ye first the Kingdom of God, and His righteousness, and all these things shall be added unto you." Dedicate yourself to performing the work of your Inner God and walking the Path, and He will organize your karma in such a way as to deliver you the circumstances you need at the appropriate time.