Be precise about what "prove it" means
Provenance is a strong tool and a narrow one. It is worth stating exactly what it does and does not establish, because a claim that overreaches is worse than none.
What you can prove: that this exact file (by its cryptographic hash) existed no later than a specific moment, that it was signed by a particular key, and where it sits in order relative to other registrations. Dated existence, integrity, a signer, and sequence.
What you cannot prove this way, and nobody can with a timestamp: that you are the legal owner, the original author, or that the idea is yours rather than convergent. A signature binds the bytes to a key, not the key to a person. Those are separate questions, settled by separate evidence.
That boundary is the point, not a caveat bolted on. In almost every real dispute about copied work, the thing you are missing is not a philosophical claim to authorship. It is dated, tamper-evident evidence that you held this artefact before the other party did. That is precisely what the steps below give you.