Bronze from the bronze age was made by smelting copper with tin in a 9:1 ratio (at that time it also had other things mixed in like arsenic and lead). You can't cold forge bronze. Its an alloy. Its possible to separate the tin from the bronze when you reforge it but the tech required to do so wasn't available until the late industrial age.

In the Bronze age copper and tin were shipped in pre-smelted billets that weighed about 50 pounds each. Most of the tin used during the bronze age came from the Cornwall area in the British isles. It was the purest and most abundant source in Europe, West Asia, and Northern Africa. Most of the copper came from Crete and Cyprus because those were the purest and most abundant sources in that area.

The alloys were made on site from the pure metals that were shipped in. In the early bronze age that was Tyre and Byblos then in the late bronze age and early iron age Carthage and Rome.

Taking control of the supply of tin was why Rome invaded Gaul and Briton.

In game how bronze is made is messed up and the ratios are way off too. It takes 10 bronze ingots and 4 boards to make a bronze buckler that would have weighed at most 1.5 Kg and increasing quality wouldn't take additional metal. It would have taken more skill and time instead.

Iron is messed up too and in the same ratios. Early iron weapons were smelted and then forged to remove impurities. They didn't hold an edge as well as bronze weapons and they were brittle and didn't last as long. The late Iron age and the blast furnace was what made the difference. Iron is far more common than copper or tin but Iron took far higher temperatures (and the addition of carbon) to be as effective or better than bronze.