How large can the bitcoin salt value be?
It's actually called a "nonce".

It is a 32-bit number so is maxed at 2**32 or 4294967296.

If the hash and data given are valid, you can always hash the block header data to get the same block hash.  If anything is changed, including the nonce, the hash will change, invalidating the block (header).

Each valid nonce is dependent upon the data being hashed and the target difficulty according to the protocol.