Copper occurs native, as metal, in nuggets and masses, most famously around Lake Superior. That is why it was first. It required no smelting, no furnace and no theory: a nugget could be hammered into shape cold, and copper beads and awls from the Near East date to the ninth and eighth millennia BCE.
Smelting, reducing copper ore with charcoal in a sufficiently hot fire, is a genuine technological threshold and appears in the fifth millennium BCE. It means the supply is no longer limited to what nature has already refined.
Pure copper is soft. Alloyed with about ten per cent tin it becomes bronze, which is far harder, casts more cleanly and holds an edge. That combination defines an age. Its difficulty is that copper ore and tin ore rarely occur in the same places, so bronze required long-distance trade in a way that nothing before it had: Cornish and Iberian tin moved across Europe to Mediterranean copper, and the eastern Mediterranean drew tin from as far away as central Asia. The collapse of those networks around 1200 BCE is one of the standard explanations offered for the end of the Late Bronze Age.
Brass, copper with zinc in place of tin, came later, made in quantity in the Roman world from about the first century BCE by heating copper together with zinc ore and charcoal, without the zinc ever being isolated as a metal.