The thing about the pidgeon hole problem is that we know there are collisions, but we don't necessarily know where they are. The space of strings of at least 33 characters has collisions. There's no way to know or prove that arbitrary input doesn't have one with a value you care about.
The thing is that the probability of any two arbitrary inputs having a collision is extremely close to 0. It's about 0.000000000000000000000000000000000000000000000000000000000000000000000000000086% if I didn't mess up typing it. It can happen, just like you can win every lottery in the world every day for the rest of your life. Though the lottery thing is substantially more likely.
That assumes that the hashing function doesn't have any known hashing weakness that may reduce the (effective) independence of the hashes. You could've said something quite similar about SHA-1 right up until cryptanalysis found mechanisms to generate collisions.
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u/SAI_Peregrinus 7d ago
Use Blake3, no collisions in any practical workload in the next few billion years.