Is rebirth philosophically possible?

Before we are born we don't exist. When we are born we go from non-consciousness to consciousness, non-existence to existence. When we die we return to the original state of non-existence. Now considering the fact that the first time we were in this original state of non-existence we were born into existence, isn't it possible that this could happen again the second time? It's rebirth but without a soul to link the second life to the first.