I agree with much of what Gmirkin has to say, but I can't agree with this. It seems quite clear that this conflation originated with Second Isaiah:
“This is what the Lord says—
Israel’s King and Redeemer, the Lord Almighty:
I am the first and I am the last;
apart from me there is no God.
7 Who then is like me? Let him proclaim it.
Let him declare and lay out before me
what has happened since I established my ancient people,
and what is yet to come—
yes, let them foretell what will come.
8 Do not tremble, do not be afraid.
Did I not proclaim this and foretell it long ago?
You are my witnesses. Is there any God besides me?
No, there is no other Rock; I know not one.”
...
24 “This is what the Lord says—
your Redeemer, who formed you in the womb:
I am the Lord,
the Maker of all things,
who stretches out the heavens,
who spreads out the earth by myself,
25 who foils the signs of false prophets
and makes fools of diviners,
who overthrows the learning of the wise
and turns it into nonsense,
26 who carries out the words of his servants
and fulfills the predictions of his messengers,
5 I am the Lord, and there is no other;
apart from me there is no God.
I will strengthen you,
though you have not acknowledged me,
6 so that from the rising of the sun
to the place of its setting
people may know there is none besides me.
I am the Lord, and there is no other.
7 I form the light and create darkness,
I bring prosperity and create disaster;
I, the Lord, do all these things.
...
18 For this is what the Lord says—
he who created the heavens,
he is God;
he who fashioned and made the earth,
he founded it;
he did not create it to be empty,
but formed it to be inhabited—
he says:
“I am the Lord,
and there is no other.
19 I have not spoken in secret,
from somewhere in a land of darkness;
I have not said to Jacob’s descendants,
‘Seek me in vain.’
I, the Lord, speak the truth;
I declare what is right.
20 “Gather together and come;
assemble, you fugitives from the nations.
Ignorant are those who carry about idols of wood,
who pray to gods that cannot save.
21 Declare what is to be, present it—
let them take counsel together.
Who foretold this long ago,
who declared it from the distant past?
Was it not I, the Lord?
And there is no God apart from me,
a righteous God and a Savior;
there is none but me.
The way I see it, Second Isaiah is record of the beginnings of the monotheistic cult of Yahweh, under the tutelage of the Persians, who were Zoroastrian monotheists. Second Isaiah is pro-Persian propaganda, likely emanating from the administration of Cyrus. The point of this monotheistic endeavor was to present Cyrus as the only possible savior and leader of the people of Judah. Each god had their own priests and cults and prophets. There was a relationship between politics and gods. Multiple gods allowed for the voices of multiple priests and prophets. The priests of one god may favor different rulers and thus put forward divine commands to side with one ruler or another. Cyrus wanted to limit these voices. He presented himself as the chosen ruler of the Judahites who was selected to lead the Judahites by their God Yahweh, who was, by the way the only God that existed, so anyone claiming that other gods had chosen a different leader were false prophets.
This, in my view, was the origins of the monotheistic cult of Yahweh. It had nothing to do with the Plato.
When the Persians fell to Alexander, however, then the Judahite priesthood had to scramble to align themselves with the new world order so as not to be overthrown. This is where the creation of the Torah comes in, with its use of Greek sources, to create an account that would have enabled the Judahites to claim that they were an ancient nation of laws who were capable of self-rule. Much of the point of the Torah and the claims of the Jews was to show that they were an ancient nation with a royal line that had a right to autonomy. This is because in the region at the time, such ancient nations and administrations were given more rights and allowed to adhere more to their own traditions. Groups who could not make such claims were more thoroughly Hellenized and brought under the control of the ruling administrations. So part of the bid for political power of the priesthood lay in their ability to show that they were the leaders of an ancient nation of laws, who thus deserved the right to govern themselves. So that's why the Judahite priests would have engaged in this endeavor to develop this history of the Jewish people and to do it along Hellenistic lines, in a way that would have been approved of by Hellenistic leaders, by drawing on the works of Plato, a respected Hellenistic thinker.
But Judahite monotheism was pre-existent under the Persians. However, it is very likely that even under the Persians Jewish monotheism was never fully established among the population of Judahites. It may have been the official position of the priesthood, but it was likely not fully adopted by the populous, who continued to adhere to their polytheistic Canaanite/Israelite traditions in diminished fashion. And this struggle seemed to continue on into the Hellenistic era.