This is the basic problem of sentience though, right? Lots of people suspect it is something like wind or rain, but we haven't gotten the physics or biology down yet.
When philosophers separate the world into 'high probability guess work' and 'logically provable laws,' pretty much all of experimental science gets put in the former bucket.
I think the level of precision in describing behavior can't be it. If we assume human minds are by definition sentient, we can imagine all sorts of hypotheticals -- plug a brain into a virtual reality with very constrained choices, and you'll I guess be able to construct a situation in which it behaves very predictably. Do it from birth, and we've chipped away at your 'lifetime' objection. I think we'll have trouble getting the ethics board to approve this one.