There's been attempts to standardize a way for a HTTPS server to say "Yes, this response really did come from me", but nothing has been really adopted.
Without the server participating, best you can do is a LetsEncrypt-style "we made this request from many places and got the same response" statement by a trusted party.
Inspiration: roughtime can be used to piggyback a "proof of known hash at time" mechanism, without blockchain waste. That lets you say "I've had this file since this time".