It's been a while since I read about zero-knowledge proofs, so I wasn't aware of the non-interactive kind. But I read up on them, and as I understand, you have to pre-commit to a finite set of participants in the protocol who can verify that you have the proof.

Which makes sense: If the evidence (that you have a mathematical proof) could be convincingly shared with absolutely everyone, it wouldn't be zero-knowledge any longer. The whole point of zero-knowledge proof is that the evidence is only useful for the recipient(s).