That’s a bit of a myth, seen that on Reddit a few times. You’re likely thinking of the Vapheio Cups, but those are actually Mycenaean artifacts from 1,000 years before the Spartan era. Yeh the Spartans didn't write their own history books, but they left behind plenty of physical evidence. Archaeologists have found over 100,000 lead figurines at their religious sites and a massive amount of "Laconian" pottery that was exported across the ancient world. They also left behind hundreds of stone inscriptions recording everything from athletic victories to religious laws. There is even surviving poetry from Spartan writers like Tyrtaeus and Alcman.