J.W's and other Bible thumpers often make claims for its antiquity, and as Leo has shown above, certain passages are very old stories/poems, psalms etc , but I do not think much of it is very early as a collected "bible", probably only after the Babylonian exile was it put together, before that it would have existed as writings amongst many, not seen as a single book as we look upon it.
With many other writings being revered as "wisdom" , which are not now considered canonical, came the need to establish a canon, and to do that it is evident that much redaction of the writings considered worthy of inclusion was deemed necessary, much being done by Ezra perhaps.
The claims made for the Bible by the WT are as suspect as the calims it makes for itself as an organization.