I didn’t quite answer your question. The same effect is true in modern times. Why do we use the term ‘modern’?
The term varies in its usage, but the point is that in the nineteenth century it was clear a new era had started.
The industrial revolution powerfully suggested that, but there is much more to the ‘modern’.
The sense of a new era was obvious even if people didn’t see why
The same happened to the Israelites and they were rapidly creating a new religious culture.
They did not properly distinguish the stream/sequence: but even Solomon is mythical.
The Mosaic record is hopeless as history
and he could not have created the materials associated with him
but the emergence of monotheists in primitive form predates the history of Israel.
The transition amplifies that and creates the Bible.
The appearance of the prophets was also a kind of indication.
The analysis is very treacherous because too many texts have been revised in the post-Exle
period. And the earlier saga as noted was very mythological. It makes sense to think Moses
had some historical basis but the overall result is not reliable history.
It is important also to see the influence of the Zoroastrians during the Exile.
Some think that the real monotheism springs from the Persian source.
I need to review myself the data here: The Bible Unearthed is very useful
(Amazon has used copies for a buck or so)
The point is no so much that the Israelites noted the transition
but that the Greeks didn’t. But their culture was transformed in the
transition centuries, especially by the mid eighth century, with
the same timing in Israel.