Well, if you really believe that she is your soul mate and are meant to be together, there is no reason why you should give up so easily. You should definitely give your very best to fight for your happiness.
However, you don't want to push her too much as it can backfire. If you have just broken up a few days ago, then you will need to be patient and take things more slowly.
Avoid calling her immediately after the break up. Chances are she will ignore you. Even if you manage to reach her now, you might not know the right thing to say for the time being.
It is best for you to take at least one month to think clearly about what you really want as well as to heal your broken heart. I believe your girlfriend will also need this time for herself as well.
Take this time to seriously consider whether you want to get her back or simply to move on in life. If possible, try not to meet her during this one month. Only contact her after this period.
If she happens to be your colleague or classmate, obviously, it is impossible not to see her everyday. In this situation, you should not pretend not to see her. You don't need to talk to her if you don't want to. In fact, you will want to minimize your conversation with her. But at least, you should still say hi and be friendly whenever you see her. This will leave your door open should you decide to get your girlfriend back one month later.