It is not a simple to answer question. If you want to know whether there is a binary string that hashes to a particular value, it may be that the only way to prove that one exists is to keep testing strings until you find one that hashes to the correct value. And if it turns out that no such string exists, that may be impossible to prove. You can in principle prove that no such string below some particular finite length exists, but it could well be impossible to prove that no such string of any length exists.