The broken remnants of a Mycenaean shrine was found under the sanctuary at Eleusis by the Greek Arch Society in the late 19th century. They also found evidence of ritual animal sacrifices, specifically pigs, which of course seems like a clue because of their association with the cult. But it’s not a smoking gun. Other than these two elements, the Mycenaean shrine has no tangible associations with the cult and this is the origin of the debate, which at this point is basically a pissing contest between archeologists. Good news is that there are several papers/journals and books that discuss the finer details of the controversy and arguments from both sides if you want to deep dive into the particulars.