The works of Hildegarde von Bingen from about 1000 AD and other religious composers are the earliest we have from Europe- mostly chant. The Inuit had no written records. Some Chinese works, or at least the traditions associated with them, go back to 2000 BC- I know little about their music.
The earliest recorded secular works also seem to be medieval (Spanish, German, Sephardic, Arabic).
We have older lyrical poetry, of course, but the tunes are lost.
A number of secular tunes from the British Isles are claimed to be ancient, but there is no factual evidence from before late 1400s for any of them that I have heard of.