I Think It's 627 BC With The Last Chapter At 487 BC.

It is currenty believed that Job was the first that was written

I find there reason to believe that it isn't that old. When listing three people, Ezekiel mentions Job after Daniel. Furthermore, the book mentions Sabeans (who came into existence about 1200 BC according to gotquestions.org) and Chaldeans. (The oldest mention of the land of Chaldea was made by Ashurnasirpal II of Assyria, who reigned 884 to 859 BC.) Notice that the Chaldeans are just "raiders" and not conquerors or invaders, meaning that this event in Job's life occurred prior to the 605 BC ascension of Nebuchadnezzar. The was Y think it happened is that there was a Chaldean (I think it's most likely Nabopalassar, because only his rebellion was successful) who, in Babylon, revolted against the Assyrian Empire and sent come of the Chaldeans loyal to him (non need to be gender-neutral, all the Babylonian rebels against Assyria were men) to raid nearby areas in order to get supplies for his revolt against Assyria.