All I'll say is you have a lot more optimism in the survivability of both the records and the ability to read them.
Imagine for example that the Persians win the war. The major Greek City states who defied Xerxes are razed to the ground and new people's are imported to serve as colonists for the Satrapy of Greece. The Greeks who surrendered, like the Thebans are left alone, and they write histories of the Persian war.
Centuries pass, and the Persian Empire fragments. Nomadic pressure and civil war lead to a breakdown in security. As the Persian garrison armies weaken, the Celts that in OTL invaded during the reign of the Diadochi, strike. With the Satrap busy in another of the Persian civil wars, the Celts find great success, burning and pillaging Greece and Asia Minor over and again. They then begin to settle, much as the Slavs did when the Byzantines nearly collapsed in the 7th and 8th century.
The situation eventually stabilises, and order is restored, but the land is depopulated. Many of the Greek City states, demilitarised by the Persians are completely decimated, their citizens now slaves to new masters, their records ash. Greece essentially becomes an ATL Galatia, where Celts rule over a mixed Greco-Anatolio-Persian population, while acknowledging Persian suzeiranity.
Centuries pass on, and more migrations bring more people groups to Greece, with new languages.
Eventually a thousand years past the sack of Sparta, the Greek language is extinct. Without a metropole to nourish them with new colonists and military support, the great Greek colonies have assimilated to their neighbouring cultures, much as happened to the many of the Greek and Punic Colonies of OTL. A noble from say, a steppe descended Turkic tribe rides past the ruins next to the village that was once Sparta. The locals speak a Celtic language and write in a script derived from Aramaic. In such a case, is it that far fetched that when asked by the noble whose these remains are, the local elders merely shrug at the engraved markings they cannot read and make up a mythical tale to explain things away? In such a case wouldn't the Persians have succeeded in wiping Sparta from history?