First, copper didn’t just come from Cyprus, also Hatti. Tin came from Afghanistan, specifically the Badakhshan region. It was mined there, then transported to Babylon or Assyria. The city of Assur (in Assyria), the namesake of “Assyrian” was known as a major tin trading center in the Bronze Age. It could be shipped to Greece, Egypt, or Hatti through one of the port cities on the eastern coast of the Mediterranean, usually Ugarit.
Source: 1177 BCE, The Year Civilization Collapsed, by Eric Cline (2011)