Lots of views on this one, I don't have one I'm rooted to but one of my personal favorites that seems to match up with the view of the universe I have in terms of the laws is that God, being all-omni-stuff, forges a soul somehow, maybe he cuts off a piece of Him, maybe it's like He's a tree who drops seeds, or maybe it's like baking cookies or something. This fragment gets stuck inside someone at a unique moment, probably conception but who knows, and stays on as a sort of mass recorder, one that does not have to follow Observer Effect.

Now, at this point the soul would be meaningless, its just storing a copy of info, and that solution is not satisfactory to me... however, there's Quantum to deal with. Since the recorder-soul item is not actually part of the Universe or impacting it at all, and since God is all Omni-stuff, it seems no problem that it could store and stretch along alternate realities. So life starts, at some Time Zero, and for that singular moment we have a single reality for that soul, a unique identity. Now time begins moving, and things begin to diverge, in many you die, miscarriage, abortion, infanticide, stuck your finger in the light socket when you were two, etc, that piece of you ends but is still recorded. Some you grow up to be a banker, a scientist, a football player, a bum, a murderer, a big expanding tree of possible life branches and when you're all done, that's all stored on the soul, a massive multi-reality total of all that you were and could of been, no what ifs available because you lived all those what ifs.

What's done after the fact with that I have no idea, but it raises some interesting 'Yourself as God' options for Final Judgment since you'd be in a unique position to assess the results of your lives, and actually still your decisions, since the brain does not really operate at the quantum level there'd be a lot of trends and all. You'd always have those freak break away situations where by an absurdly improbable quantum event you changed your mind, but if there was say, on a given moment, a 99.9999% you would decide to go for a walk, only 1 in a million of the divergent realities would have that not happen and quantum or not most stuff occurs by classic cause and effect at the macroscopic level.

I'm moderately fond of this soul option because it gives a reason for their to be a soul that specifically can get away with being undetectable but isn't pointless, after all if something interacts at all with the physical universe it leaves a footprint by interacting, and if it doesn't, then it serves no purpose except as a copy, well we already know that by current laws it is possible to make a copy, to any reasonable standard of accuracy, of a human mind, there's no real need for God as omni-dude there, some reasonable benevolent Super-alien(s) could do it, if we had the tech and stumbled across some world with non-high-tech persons its not a stretch to think we might decide it right and proper to make copies of their lives to be stored or even resurrected. But that just hits the "Is a copy of me really me" problem and then you run in simulated realities and the Simulation Hypothesis and the Omphalos Hypothesis for that matter, and none of it accounts for the option of alternate realities which while not yet proven, the Many-Worlds Interpretation is pretty solid and you still have to deal with the issue of whether all those alternate-yous each has an individual soul or not, plus free will and all becomes rather redundant since you pretty much make every decision anyway. Of course it has its own philosophical problems and no proof, but it is at least reasonably consistent with my view of the Universe. Where exactly this is all stored is another matter, might as well call it Heaven.