Hmm, I've always been a rock-hard atheist, so naturally, I haven't believed in a 'soul' or even some external 'consciousness' or 'essence,' at least not something that outlasts the brain.
But for the last couple of weeks, I've had much more unique thoughts about this. I think it's possible; there is so much mystery in existence. For example, according to quantum physics, nothing really fundamentally exists; it's all just very abstract probabilities. This, of course, goes against all logic and our observations from our human perspective.
Also, these thoughts about 'time' as a dimension of our reality might interest you: