It's worth pointing out that while modern hash functions are believed to be infeasible to unscramble (technically, to require exponential time), none have been proven so. In fact, proving the mere existence of such a function would prove P!=NP.
If you can prove P = NP, then you have proved that no secure hash functions exist. (This is the contrapositive.)
(For a fun angle not related to complexity, the algorithm itself could be so large that it wouldn't fit in the observable universe without breaking the Bekenstein bound.)
And it has been a long time since I did proof theory, but is there the possibility of a non-constructive proof but no actual examples no matter how long you keep enumerating algorithms? Or a non-constructive proof, but no constructive proof? In that case there could be a "perfect heuristic"...