How did we cut our hair and nails without metal objects? Metallurgy, like speech and writing are probably available to man since the fall, around 6000 years ago and certainly since the flood approximately 4,400 years ago.

Good point.

The Bronze Age is a historical period lasting from approximately 3300 to 1200 BC. It is characterized by the use of bronze, the use of writing in some areas, and other features of early urban civilization. The Bronze Age is the middle principal period of the three-age system, between the Stone and Iron Ages.^[1] This system was proposed in 1836 by Christian Jürgensen Thomsen for classifying and studying ancient societies and history. Worldwide, the Bronze Age generally followed the Neolithic period, with the Chalcolithic serving as a transition.
The periodisation of the Bronze Age is generally ended with the Late Bronze Age collapse, a time of widespread societal collapse between c. 1200 and 1150 BC. This collapse affected a large area of the Eastern Mediterranean, including North Africa and Southeast Europe, as well as the Near East, in particular Egypt, eastern Libya, the Balkans, the Aegean, Anatolia, and the Caucasus. It was sudden, violent, and culturally disruptive for many Bronze Age civilizations, and it brought a sharp economic decline to regional powers, most notably ushering in the Greek Dark Ages.
An ancient civilization is deemed to be part of the Bronze Age if it either produced bronze by smelting its own copper and alloying it with tin, arsenic, or other metals, or traded other items for bronze from producing areas elsewhere.
Bronze Age civilizations gained a technological advantage due to bronze's harder and more durable properties than other metals available at the time. While terrestrial iron is naturally abundant, the higher temperature required for smelting, 1,250 °C (2,280 °F), in addition to the greater difficulty of working with the metal, placed it out of reach of common use until the end of the second millennium BC. Tin's lower melting point of 232 °C (450 °F) and copper's relatively moderate melting point of 1,085 °C (1,985 °F) placed both these metals within the capabilities of Neolithic pottery kilns, which date back to 6,000 BC and were able to produce temperatures of at least 900 °C (1,650 °F).^[2] Copper and tin ores are rare since there were no tin bronzes in West Asia before trading in bronze began in the 3rd millennium BC.