So, I haven't read up on this quantum attack stuff, and I don't know what Kairos is referring to, but setting aside quantum computing for the moment, breaking a cryptographic hash would simply require being able to find a hash collision, finding another input to a hash function that generates the same hash. It wouldn't require being able to reconstitute the original input that produced the hash. That collision-finding can be done -- given infinite conventional computational capacity, at any rate -- simply from the hash; you don't need additional information.

Nobody is wanting to make a magical algorithm that gets the input to the hash.

I mean, there's provably at least one person who does, but there are infinite inputs that lead to the same hash.

Breaking a hash is being able to easily create new input data that leads to the same hash (with or without the constraint of needing the original input data)