Is there a digital equivalent to the Great Seal of the United States?
Is there a way, then, of doing something like the above, but without the need for a central authority? 


Why, yes, we do have a way to solve that problem - we refer to it as a 'digital signature'

Here's how it works:


Select a signature algorithm, and come up with a public/private key pair for a signature algorithm
With the private key, generate a signature of the document (possibly with the time stamp and anything else you find relevant).  Affix the above hash, together with the timestamp, to the document.
When someone wants to authenticate a document, simply get the public key, and check that the signature validation algorithm, together with the document and the timestamp, states that the signature verifies.


The fundamental property of a signature algorithm is that, while it is easy to sign any document you want with the private key, you cannot sign any document (where "sign" means generate a signature that verifies with the signature validation algorithm and the public key).

Common signature algorithms in use today are RSA, ECDSA and EdDSA

Of course, one step I didn't go into is "how, in step 3, does someone get the public key" and "how do they know that the public key they get is actually the signer's, and not some attackers"?  These are valid questions, with good answers; but I think I'll leave the exploration of that for another question...