Prove there was a Persian Empire.
No problem. Herodotus (one of the first historians, and accepted by his peers) documented (in The Histories) many of the Greek-Persian wars, as well as much of the Persian Empire Kings (similar to our “Melachim”). If you want a Jewish source, how about Daniel?
Later Persian Empires (such as the Sassanids) are even easier. Procopius documented the fights of the Romans against the Persian Empire, as well as the Babylonian Talmud (there’s a source that even you would accept!)
How about coins of the Persian Empire that still exist?