Technically correct. History is about written history. It is separate from archeology, which covers most of the rest.
Written history began in the 4th millennium BC, concurrent with the invention of writing. And yes, it happened in the west first. The history of China was hampered by its first emperor, who ordered all written history prior to his reign destroyed.
Sumerian writing was at least 600 years earlier than your 400 BC date. As were written records of Egypt.