As others point out, you made a critical error in this model.

If you aren't the only person to have the private key, then the wallet is no longer yours, and yours only. You merely have equal control over the same wallet. Or to put it simple: the only way to prove sole ownership is to be the sole person controlling the private keys.

If you want to prove you owned it first, and it was stolen or given away or compromised, then you must find a way to prove that you used it first.

In your model, you could create a wallet and immediately "Stake" a Bitcoin address on this forum, signing from it. It doesn't prove you were the first owner though, just the first to use it or to attempt to provide evidence of owning it.