Can hash values theoretically be used as a form of super file compression, given enough computing power?

I read that theoretically each hash value is unique to a particular file, so if that's true a computer could reconstruct a file by using "brute force" to cycle through all possible combinations of data until it matches the hash value... impractical, but what if the algorithm, file length, etc. were known- could a computer reverse the algorithm to reconstruct the original file? Would it be theoretically possible to "store" for instance, 32MB of data in a few bytes?