This is more of a philosophy question. As it is, it is one of the largest unanswerable philosophy questions in existence: how do you prove or disprove the existence of a deity or other metaphysical entity. So the answer to your question is simply "you can't." Philosophers have spent thousands of years pondering this question, and the answer is always the same: either "you can't," or that philosopher is selling something.
Ironically, having a soul prove a deity exists is easier than proving one does not exist. While both are still in the "you can't" range, all one has to do is provide one example of a deity existing and it refutes the claim "deities do not exist." To prove that a deity does not exist requires proving a negative. One must prove that there is no possible way for a deity to exist.
To demonstrate the difficulty of this, consider the case of the absent creator, which creates the physical world, then goes on vacation and lets it run until the end of days. This creator then comes back and does something. There is no physical way to prove this is not the case. We may use abduction to come to the conclusion that "there are no deities" is true because it is the "best" hypothesis, but that's a far cry from what you ask.
Indeed, the closest you could get would be if the "soul" provably came from some primordial soul-mass as in Secespitus's answer, and returned to it. Interestingly enough, that is a paraphrasing of the fundamental cosmology of Hinduism, that we are all the Godhead, just divided because the Godhead wanted to be divided, and that one day we will all reunite. It is also at the heart of the greeting, "namaste," which we most often hear from yoga practitioners. The meaning of that is often traced back to the idea of bowing to the "divine spark" in you, and in us all. It is also the structure often found in the druidic religions regarding the divine Earth Mother (e.g Gaia), to which we all return.
So the related question is "how do you define 'divine?'"