I am sure the question of deciding what is commemorative or not will blur with ancient coins. As they are not usually called "commemorative" in catalogs but they may picture something or someone to commemorate.
But for e.g. this - https://en.numista.com/catalogue/pieces124575.html will fit the "commemorative" issue.
Under the "modern" understanding of commemorative coins, some countries in Europe have been producing them from the 15th century, probably even earlier. https://en.numista.com/catalogue/pieces155210.html
A rough guess would be Gold staters minted by Alexander the Great in the various new cities he set up in Asia Minor, Middle East and central asia between 335 and 330BC
Then Roman coins celebrating capitulation of Greece and Carthage in 146BC. Romans loved issuing coins with the word "CAPTA" on them, meaning a place had been added to the Republic/Empire.
I love coins. Especially silver, gold and anything really old.
Member of the Royal Numismatic Society of New Zealand and the Auckland Numismatic Society