the literature created by the Sumerians left its deep imprint on the Hebrews, and one of the thrilling aspects of reconstructing and translating Sumerian belles-lettres consists in tracing resemblances and parallels between Sumerian and Biblical motifs. To be sure, Sumerians could not have influenced the Hebrews directly, for they had ceased to exist long before the Hebrew people came into existence. But there is little doubt that the Sumerians deeply influenced the Canaanites, who preceded the Hebrews in the land later known as Palestine’ (Kramer, 1981:142)
This theory is pretty credible. There a great deal of scholars which entertain this idea who are collectively known as Panbabylonists. This seems to raise the ire of many purists who would like to believe that Genesis was influenced by God alone.
In my opinion, however many fail to consider the idea that perhaps sections of Genesis were not derived from other texts such as the Epic of Atra-hasis, or the Enûma Eliš but instead are a polemic, corrective response to these alternate creation narratives. For example in Enûma Eliš mankind is created because the gods are lazy and do not want to work. They therefore create mankind in order to work the earth and bring them (the gods) offerings. Instead, in the creation story of Genesis, the earth is created for mankind and they are placed as kings over creation. It is almost as if Genesis is saying "we all know that the earth was created in 6 days and that it was created from these waters. We all know a mound was formed and then creation proceeded and so forth, but let me tell you WHY it was created because you others have all gotten the why wrong. Oh, by the way, Yahweh is more powerful than your puny gods." This is tentatively coming to be known as the framework view, interpretation or hypothesis. Accordingly, how one regards this idea of Panbabylonism tends to be closely linked with how an individual interprets Genesis.
Viewing Genesis as a response to creative texts of other cultures also allows us to preserve the ideal that God divinely inspired Genesis - specifically as God's response and corrective to the widely agreed upon (at least by ancient Mediterranean people) creation events. Thus, it is plausible that Enki and Ninhursag influenced Genesis 2 and 3, but perhaps not in the way you would think.
The view one takes on the credibility of the assertion is going to depend largely on one's presuppositions and level of allowance for the Bible text to speak for itself.
If the Torah (Law, i.e. "teaching" is the idea in Hebrew, not just the actual commands and prohibitions), which includes Genesis, was formed contra what critical scholars claim, and instead ...
- was in fact essentially singly authored by Moses (with possibly a few final editorial editions by Joshua [about Moses's death? Dt 34:5-8], who is recorded to have added further information to the Law in his own time in Josh 24:26, though that only sets a precedent for his additions, as the passage itself is more specific to the renewed covenant vows of the people in v.19-23), and
- was largely "dictated to Moses by God" (quoted from above link on Mosaic authorship), some being written both before ever ascending to Sinai (Ex 24:4), some upon Sinai (actually stated there to be given by God initially; Ex 24:12), and most likely after the fact during the tabernacle meetings with God (of which Joshua was also privy to; Ex 33:7-11), and
- was essentially complete at the time of his death, and entrusted to the priests for reading to the congregation every seven years (Dt 31:9-13; whether this was ever practiced or not in its entirety is questionable—later tradition only read "selections from the Torah."), ...
then there is no credibility to the assertion at all (disclaimer: this is my view). This indicates that the history contained in Genesis, Scripture declares God revealed to Moses. Such an account from "the God of truth" (Isa 65:16), the One who is and does right (Gen 18:25, Ps 7:9, 11:7), and was there (Gen 1:1), is then the true account of creation, which being mankind's history, those events did become a basis for the various morphed forms of that history by various cultures across the planet (including Sumerians).
Of course, if one rejects points 1-3 above (in line with critical scholars), and rather favors more direct pagan influence on the Hebrew scriptures, then there is at least plausible credibility for the assertion that the Sumerian works influenced the Hebrew works. There is of course some pagan influence, as the Bible addresses aspects of paganism both in the nations around Israel and within Israel itself, but that is a different category of influence than what is asserted with the early chapters of Genesis—the former idea condemns the paganism, whereas the latter would attribute pagan ideas as an "imprint on the Hebrews" (per your quote), rather than looking further back to the history itself that imprinted them both.
So presuppositions drive how one reads the evidence, and thus will lead to differing views on the credibility (and nature of) the relationship between the two.
With any theory like this its just as credible that the influence goes the other way. The argument that the Sumerians could not influence the Hebrews directly is bunk, in that perhaps they could not directly influence the author of Genesis, but since they would have been contemporary with Abraham they could have influenced the stream of Hebrew thought at an earlier stage. But this is just the problem, namely, that Abraham and people associated with him could just as well have influenced them. Furthermore, if we conceive the story as coming to the author through a tradition going back to Abraham, and possibly through Abraham back to Adam, or some such, then both the Hebrews and the Summerians would have been influenced at a much earlier time than either of the literary remains. In short, nothing can be proven one way or another.
But more importantly than any of this, if you actually read these Pagan epics that scholars love to claim are so similar to the Biblical stories, you will find that the differences stand out much more than the similarities: the gross polytheism, for instance, or the mythologizing of characters to the point that they're more like Superman than a real human character with flaws.
I would say impossilbe because:-
1 Chronicles 16:26 All the gods of the peoples are worthless gods,. . .
Psalm 96:5 All the gods of the peoples are worthless gods,. . .
Isaiah 2:8 Their land is filled with worthless gods. They bow down to the work of their own hands, To what their own fingers have made.
Isaiah 37:19 And they have thrown their gods into the fire, because they were not gods but the work of human hands, wood and stone. That is why they could destroy them.
Besides the gods of Sumer, the Bible Shiner, were not invented by humans until AFTER the Flood of Noah's day; Gen. 5 onward.
The myths of Sumer were taught in Egypt but rejected by Moses the penman of Genesis, beside God would not alow pagan myths to soil his word The Bible.
The pagans took concepts from the Bible account via the confusion of Babel onward and retold them using various gods and demigods.