As most numismatists know coins first appeared around the 6th century BC in three separate places Lydia, India and China.
Lydia is hailed as having been the first to mint coins in 650s-ish BC. The first Lydian coins were beanlike, stamped with a lion head and made out of electrum.
The oldest known Indian coins are from 450BC and were punchmarked by circular and oval shapes. The coins themself were more like bars, bent by the punchmark process .
China 'coins' are totally different from Lydia and India. China started minting 'coins' 100yrs after the Lydians, they were in the shapes of miniature knives, forks, hoes and spades. Another important difference is the tools being used as currency were made in molds instead of being struck with dies such as was used every where else.
Chinese Knife Coin
In conclusion, we are sure they all starting producing coins independently because they were all made by separate processes and were all of quite a different design.