Before your 'soul' formed, your brain had to grow to a certain volume and develop certain layers of cortex. Your 'soul' wasn't born into your body, your body (read brain) put your 'soul' into itself. (I'm going to asume that for you a 'soul' is something like a selfaware psyche, since you mentioned experience of the self as the defining characteristic.)
And I don't know what religion's or myth's form of reincarnation you are talking about but I haven't read about any that actually believes in transport of 'souls' into a (newborn) body. The most prominent ones will believe that karma can be reborn into new life (and that's a concept that's not even too wild if you are willing to put sense into it, but I don't want to deroll into this any further).
Edited by Yoshimi, 03 August 2012 - 04:56 AM.