I don't think it was a question of proving them to be myths, it was a question of the inability to prove the claims the mythical gods existed.
The claims of their existence were highly visible. Such as the gods lived in a palace on Mount Olympus. After many thousands of people had climbed Mount Olympus and did not see the palace of the gods, nobody could offer acceptable proof that the palace existed.
It wasn't that they were proven to be a myth, it was that no acceptable, lasting proof could be found to prove that they were gods.
The choice had always been was it true religion or was it false religion. A negative can not be proven. The burden of proof had always been to prove that it was true religion. They are remembered as myths only because the stories and scriptures were entertaining stories and very good examples of literature. But, the various stories were not proven to be true. So, they are simply interesting stories with no lasting proof to show they are true.
It was not that they were proven to be myths, it is that no valid proof is known to show it is true.