Which was the first empire to have a naval fleet?

The first empire to have a naval fleet is most likely the Greeks. The Phoenicians (which is now modern day Syria, Lebanon, Turkey and parts of Israel) traded with Greeks. They trade woods and dye. The phoenicians were instrumental to the building of Greek fleets, there were the ship builders.

Up until this day, the Greek Merchant Navy controlled the world's largest merchant fleet, in terms of tonnage with a total DWT of 334,649,089 tons and a fleet of 5,226 Greek-owned vessels.

“The first dateable recorded sea battle occurred about 1210 BC: Suppiluliuma II, king of the Hittites, defeated a fleet from Cyprus, and burned their ships at sea.” Since this is the first recorded sea battle, I assume the first naval fleet belonged to Suppiluliuma II, king of the Hittite Empire.