I can't give an answer but I think this would be very early in recorded history. Written Greek & Roman history, I think, will be full of them. They must surely predate Greece & Rome.

You get them in antiquity. Off the top of my head, the Romans had the Nero redivivus theories that claimed that Nero was still alive and would come back to rule Rome. This actually had some impact, as we got what we call Pseudo-Nero(s) who would show up and claim to be Nero, and some of them would get some sizable followings.

With less mythology attached, we get a lot of Pretenders who claim to be so and so's lost son, and try and seize thrones. One of the more infamous cases from antiquity was the case of Pseudo-Philip, or Andriscus, who claimed to be Philip VI of Macedon and was the direct cause of the Fourth Macedonian War.

Then you have incidents like the mutilation of the hermae and the mimicry of the Mysteries in fifth century Athens which caused a lot of conspiracy theories and a lot of witch hunts. Everything from the Spartans, or some other group, having secretly invaded, to either pro-democracy, or anti-democracy political factions sending a message, to named individuals of importance directly causing these events (something that Alcibiades was greatly affected by).

Or stories that the Carthaginians were conspiring with the Persians because two famous battles seemed to have happened on the same day. https://en.wikipedia.org/wiki/Battle_of_Himera_(480_BC)

When you mix in a lot of emotion, a lack of verifiable information, and a period where gossip could spread without much fact checking or wholly reliable news sources, you get a lot of things like this.