There are timestamping services out there, some of which may be free. It should (I think) be possible to basically submit the target site's URL to the timestamping service, and get back a certificate saying "I, Timestamps-R-US, assert that the contents of
https://targetsite.com/foo/bar downloaded at 12:34pm on 29/5/2025 hashes to abc12345 with SHA-1", signed with their private key and verifiable (by anyone) with their public key. Then you download the same URL, and check that the hashes match.
IIUC the timestamping service needs to independently download the contents itself in order to hash it, so if you need to be logged in to see the content there might be complications, and if there's a lot of content they'll probably want to charge you.