Though the statement is sort of true (but not really) it conflates and misrepresents a number of aspects of the early history of Judaism.

Babylonian and Akkadian mythology

Babylonian describes a culture, while Akkadian is a language. Babylonian can also refer to the Babylonian dialect of Akkadian, which was the language used to write many major texts in the latter days of the Mesopotamian empires. The reason the language and culture are important is that we think much of the Hebrew Bible was written in Babylon, during the Babylonian Exile (587/6-539 BCE). Some major sections of the Hebrew Bible are thought to date to this period, of which Genesis 1-11 are important because much of it is based directly on Babylonian texts (Gen 1 on Enuma elish, Gen 2 maybe on Adapa, Gen 6-9 on tablet 11 of Gilgamesh, Gen 10 on the Assyrian king lists, Gen 11 on the city of Babylon). Some parts of the Hebrew Bible are definitely older and natively Judahite/Israelite, while other parts are borrowed from the wider West-Semitic cultural continuum of which early Judaism was an integral part. (For an excellent and extensive analysis of this topic, see Smith [2002], The Early History of God.)

So insofar as you can distil the Hebrew Bible down to an 'essence', it's more a complex layered tapestry with different strands weaving together - and even then, most of these strands are 'authentically' Yahwist - than something deriving from a singular (Mesopotamian) tradition. On the other hand, some of the key texts (like Genesis 1) are definitely Mesopotamian in origin, and the overall influence of the Mesopotamian scribal tradition on the development of the Hebrew Bible should not be underestimated.

Hebrew/Yahwist elements

This is a tough one. Hebrew is just the language, though it's occasionally used to describe the culture of the biblical authors. Yahwist is used to describe the people instrumental in making Yahweh the head of the local pantheon and then turning it into a monotheistic religion, so in that sense it's a bit of a self-evident truth (of course Yahwist elements are part of a collection of texts promoting Yahweh).

Calling the Hebrew Bible something "with Hebrew/Yahwist elements" is a bit disingenuous, since it's the Yahwist text, and as we have seen already, the parts taken from other cultures don't even make up a huge part of it. It's like saying that Romeo and Juliet is just Ovid's Pyramus and Thisbe with Shakespearean elements - sure, in a strict, technical sense from one particular perspective that's true, but it misses a lot of the nuance that actually went into the work (e.g. setting, language, metre, dramaturgy, and so on).

constructed for establishing a religion

This assumes that early Judaism was an artificial religion. This is simply untrue, and ignores the centuries of development from polytheism, through henotheism, to the ultimate monotheistic form of the religion. (I'd strongly recommend Smith again for more on this: his 2000 book The Origins of Biblical Monotheism.)

to help control a Hebrew state under Persian rule

Now this is broadly speaking true: a major part of the development of Judaism happened in the early Persian period, under the religious liberalism of Cyrus and his successors. And the Hebrew Bible is pretty clear on this, as you can read in the books of Ezra and Nehemiah. But the biblical canon wasn't finished yet at this point, and we see major developments in theology as well as political ideology in this period - for example, Trito-Isaiah (i.e. Isa 56-66), which became a theological pillar for Christianity. At the same time, it is clear that the biblical authors were tremendously well-disposed towards the Persians: the 'messiah' (the traditional king of Israel, later reinterpreted to refer to Jesus) in the Persian-era parts of the book of Isaiah is Cyrus the Great - explicitly so. As a further counterpoint, the actual practice of Judaism during the Persian period differed quite a bit from the biblical prescriptions (for this, see Knowles [2006], Centrality Practised).

There's really too much to unwrap in a single comment, but I'll be happy to expand on anything you might be interested in!

I've divided my response until multiple sections based on comment length requirements.

Part One:

Aight. This is going to be long. So, let's start at the very beginning~

​

Enuma Elish, also known as the Babylonian Epic of Creation, the Babylonian Genesis, or the Seven Tablets of Creation, was composed in the early second millennium BCE, either under the rule of Sumula-el (reigned 1936 -1901 BCE) or that of Hammurabi (1792-1750 BCE).

It opens with the line “When skies above were not yet named nor earth below pronounced by name, Apsu, the first one, their begetter and maker Tiamat, who bore them all and mixed their waters together, but had not formed pastures, nor discovered reed-beds.” First there is nothing, but then land and sea are created by Apsu and Tiamat. This is paralleled in Genesis 1: first there is nothing, and then God creates the land and the sea out said nothingness.

This initial creation is followed by the breakout of war between the gods. The battle eventually comes down to a showdown between Tiamat and Marduk, the king of the gods and patron of Babylon. Marduk wins the battle with Tiamat and from her corpse, or, “her waters,” he creates the land and the earth and the sky.

In both Enuma Elish and Genesis 1, the existence of a primeval watery chaos before all else is emphasized. In Enuma Elish, this watery chaos is personified, or perhaps deified, in Tiamat. In Genesis 1, that chaos is described with the word te-hom, a word clearly phonetically related to “Tiamat.”

As for the rest of the Epic and its parallel content, Marduk creates land, then sea, then sky, then heavens, day, night, the sun and the moon, agriculture, and finally, man, created from the blood of a god. In Genesis 1, God creates first water, and then the sky and heaven and days and nights, and then land, sea, agriculture, the sun, the moon, life, and finally, man.

Marduk required seven tablets, and the God of Genesis? Seven days.

There is an 18th century BCE Babylonian epic called the Epic of Atrahasis. It begins with creation. In the beginning, Enlil, the head god, makes all the other, lesser gods do intense agricultural labor for him. They grow tired of it, and turn against Enlil. However, Ea intervenes and suggests that they create humans to do the work in their stead.

To create the human, the gods slaughter a god, and mix the flesh and blood of that god together with clay from the ground. Ea enlists the help of the womb-goddess Belet-ili in the carrying out of this procedure, and it is proclaimed that “a god and man will be mixed together in clay…let a ghost come into existence from the god‘s flesh, and let her (Belet-ili) proclaim it as his sign.” All went according to plan, and man was created to take over the gods' arduous labor.  

Genesis 2:5-7 reads “No shrub of the field was yet in the earth, and no herb of the field had yet sprung up…and there was not a man to till the ground…Then the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.” The name “Adam” is derived from the word adama, or “from the ground.” Both Adam and Atrahasis are created through the union of god and earth for the purpose of carrying out agricultural labor.

This Epic also has the gods try to wipe out humanity with a flood but then Ea decides to save one guy (Atrahasis) and his family by telling him to build a boat. So that's...Genesis 2-9.

There is another ancient story, this time, a Sumerian paradise myth called Enki and Ninhursag; Enki is the Sumerian water god, Ninhursag is the Lady of Life, and it takes place in the paradise of Dilmun. The main action begins when Enki impregnates Ninhursag. Ninhursag has a daughter called Nimmu, who Enki then impregnates, who has a daughter called Ninkurra, who Enki impregnates, who has a daughter called Uttu.

At this point, Ninhursag realizes what Enki is doing, tells Uttu what's going on, and not to sleep with Enki unless he offers her a gift of cucumbers, apples, and grapes. Enki finds out about this, brings Uttu the fruit, and sleeps with her. Ninhursag gets angry and takes Enki’s semen from Uttu’s womb before she can conceive, and uses it to grow eight plants which she forbids Enki to eat.

Enki, being Enki, decides to eat the plants, grown from the semen with which he impregnated his great-granddaughter, enraging Ninhursag. She curses him, saying that, “Until his dying day, I will never look upon him with life-giving eye,” and promptly disappears. Enki then begins to die, which upsets the other gods. They then send a messenger to find Ninhursag, and convince her to restore Enki to life. She returns in time to save him.

To heal him, she orders him to lie with his head against her vulva, and tells him to name each body part which is causing him pain. For each part he names, she causes a deity to be born in order to heal it. The second to last part named by Enki is his rib, or ti in the original Sumerian. To heal his rib Ninhursag creates the goddess Ninti, or Lady of the Rib. When Ninhursag is finished, Enki is cured.

Genesis 2:21-23 reads “And the LORD God caused a deep sleep to fall upon the man…He took one of his ribs…And the rib, which the LORD God had taken from the man, made He a woman…And the man said: ‘This is now bone of my bones, and flesh of my flesh; she shall be called Woman, because she was taken out of Man.’” In the Enki and Ninhursag story, the pertinent passage reads “‘My brother, what part of you hurts you?’ ‘My ribs (ti) hurt me.’ She gave birth to Ninti out of it.” In Genesis a woman is created from the rib of Man for Man by God, and in Enki and Ninhursag, a female deity is created by another female deity to save the life of a male deity via his rib.

Genesis 3:20 reads “And the man called his wife’s name Eve; because she was the mother of all living.” The name Eve, hawwa, is derived from the roots hwy and hyy, both of which were used in northwestern Semitic languages as roots for words pertaining to life; said roots may be found in the Amorite, Ugaritic, Phoenician-Punic, and Hebrew languages. This signals that the name of Eve is symbolic to her status as a life giver. Ninhursag’s alternate title (she has many) was Nintu, or Lady of Life.

So at the very beginning, you see a not necessarily deliberate usage of cultural elements in constructing an Israelite cosmology, but that certain tropes: gods creating the world out of a watery primordial nothingness, the number 7, man as a union of earth and god, the rib as a fixture of life, held vast cultural capital throughout the Ancient Near East, and would have been recognizable to their initial audiences, probably in oral form.

A little out of the wheelhouse, but Qumran literature was distinctively influenced by the reception of astronomical data from Babylon, coinciding with the same type of influence appearing in contemporary Greek texts. For instance, Annette Reed in her article "Writing Jewish Astronomy in the Early Hellenistic Age: The Enochic Astronomical Book as Aramaic Wisdom and Archival Impulse" (in DSD 24) compares different Enochic texts in Qumran with the conclusion that, even at its earliest, the construction of the new Enoch text relied upon data originating in Babylon.

Katharina Volk makes an analogous point in her book Manilius and his Intellectual Background regarding Aratus' Phaenomena. She claims that this didactic poem about the constellations originated during an "unprecedented flourishing of Greek mathematical astronomy, fuelled by contact (following the conquests of Alexander the Great) with Mesopotamian observational records and methods of calculation, by the development of trigonometry, and by the patronage offered to scientists by powerful rulers." (Volk 2009: 25-26).

There were clear impacts of Babylonian influence in the composition of the biblical (and parabiblical) texts. Granted, these are more relevant to later Judaism than to early Judaism, but I think the point I'm trying to make is that we don't need to establish a narrative of history when we see influences pop up in certain unique ways.

What a terrific thread!

Thanks to all the scholars contributing!