The basic claim of Robert Karl Gnuse in The Elohist is that the presumed source document of the Torah called the Elohist or E was composed in the 7th century to meet a specific need. That need was the loss of religious meaning by the exiles from Northern Israel following the fall of Samaria in about -722. So 7th century would be at least a couple decades after that event.
One of his main arguments for this is the theological idea present in E that God is majestic and distant, but available to people in places far from Samaria and Bethel. The more primitive idea was that God was local. (See the story of how Naaman thought he had to carry dirt from Israel back to Damascus in order to worship Israel’s God in 2 Kings 5:16.) But in E God approaches the fathers in Mesopotamia, in the Transjordan, in the Negev, in Egypt, and in the wilderness. Gnuse believes this is meant to reassure the exiles that God is still their God even away from Israel.
This makes for a coherent theory when combined with his observations that many of the problems with E as a source are resolved if the Yahwist used the Elohist and fused it with his own narrative. But any dating in which the Yahwist came after the Elohist could work with this idea.
The idea that E had to be composed after the fall of Samaria is interesting and possible, but doesn’t fully convince me. That a major theological theme of E fits with this date is suggestive but not any kind of scientific evidence. We reinterpret old stories all the time to make them relevant to today. So just because a story is relevant to a particular time, does not mean that it had to be written then.
Gnuse has a concluding chapter about the relevance of the Elohist for today. He refers to the idea of a more distant and hidden God fitting with modern existential alienation. He refers to the large number of refugees and displaced persons in our day. But you could reduce much of Gnuse’s argument to absurdity by claiming that this means the Elohist had to write in our time.
I do not point this out to completely overthrow or devalue Gnuse’s work. I found a great deal of helpful interpretation in his discussion of individual passages from E. His date for E does not vary that far from my own. I would look for it to have come into existence as a coherent work about the same time as the ministry of Hosea.
I base this on the fact that no one seems to have attacked the bull image at Bethel before this time. Elijah and Elisha seem to have worshiped at Bethel. Elisha supported Jehu’s coup, but Jehu continued to support the bull cult. Even in Amos, where there is conflict with the Bethel priesthood, we find no criticism of the bull image. Hosea and the Elohist are first to stand against this.
The violence in the story of the golden calf in E (Exodus 32:26-29) might reflect the violent conflict of priests in Hosea 6:8-9.
So I would date the Elohist and then the Yahwist a few decades before Gnuse would. But it is not a huge difference.
It is easy to get confused when talking about the documentary hypothesis. Some of us do not think the documents were themselves unsourced. An example would be Deuteronomy. Our Deuteronomy is not the book found in the Temple (2 Kings 22:8). That proto-Deuteronomy became the basis for adding further (old) material and theological shaping by Baruch or someone like him who produced our Deuteronomy. This leaves room for much material in D that is way older than the end document.
I assume something like that in regard to E. The Covenant Code in Exodus 20-23 seems older than the late 8th century. Hosea may have based what he said about Jacob and Moses on oral tradition or a proto-Elohist document. There is evidence of some similar development from older sources in both J and P.
So my point is that we should not overestimate the importance of when the documents themselves were composed. There are signs of great antiquity for some of the material in even definitely post-exilic documents like 1 and 2 Chronicles
The analyses of the age of the material becomes very complicated in the case of a chapter like Exodus 32. “There clearly was an old story promulgated by the kings and official priests about how the bull images represented divine deliverance from Egypt. There was likely an older, truer story that they built upon. There seem to be traces of both those layers in Exodus 32. But there is also a late layer that makes the attack on the bull cult at Bethel explicit.
The reason these questions are important is that in our age of skeptical, postmodern and minimalist tendencies there is a strong temptation to talk about an author like E as the creative inventor of a history that never happened. There was no doubt some invention in the name of polemics and relevancy, but authors worked with tradition. So I see no reason to abandon the quest to figure out what really happened. History is not just a literary construct.