The evidence is that (according to another book, The Noma Guide to Fermentation) there is no known mention of fish sauces in south/east Asia before 7th century

The evidence is that (according to another book, The Noma Guide to Fermentation) there is no known mention of fish sauces in south/east Asia before 7th century AD, while in the West it's well documented starting in the 5th century BC. The Noma Guide to Fermentation is however not an history book and is not written by historians, and anyway that's not hard evidence.