The Jews were well versed in Mesopotamian culture having lived in Babylon in captivity after the fall of Jerusalem in the sixth century BCE. Gilgamesh was an epic poem that likely had extensive influence on the culture of different civilizations in the Ancient Near East similar to the wide dispersion of the Homeric epics with Greek expansion and conquest. According to Jeffrey Tigay, the latest known tablet of the Gilgamesh cycle is from the second or first century BCE and Gilgamesh separately is mentioned in another second-century cuneiform text (Evolution of the Gilgamesh Epic, p. 251; Bolchazy-Carducci Publishers, 2002). It is possible that Berossus reproduced some of it in his Greek compendium of Babylonian history, like he did many other cuneiform texts (such as portions of the Sumerian King List).
Aelian (second century CE) gave an otherwise unknown birth narrative about a certain Babylonian king Γιλγαμος, which may derive from Berossus or some other Hellenistic source, with the baby Gilgamesh being saved from death by an eagle snatching him from a fall off the city wall. Matthew Goff’s “Gilgamesh the Giant: The Qumran Book of Giants’ Appropriation of Gilgamesh Motifs” in DSD, 2009 has a thorough discussion of this topic. The name גלגמיס appears in the Book of Giants (4Q530 II 2, 4Q531 Frag. 17 12) in the Enochic corpus, alongside other named characters linked to the Gilgamesh cycle. Two other contemporaneous Enochic works, the Book of Watchers and the Book of Luminaries (both from the third century BCE) have links to Mesopotamian traditions, with Enoch’s world journey reflecting motifs from the Gilgamesh story. For the latter, see Kelley C. Bautch’s A Study of the Geography of 1 Enoch 17-19: ‘No One Has Seen What I Have Seen’ (Brill, 2003).
Irving Finkel has a very detailed hypothesis in “The Ark Before Noah” about how Hebrew speakers in exilic and post-exilic Israel under Babylon would have come to read cuneiform versions of Gilgamesh before producing Noah’s Ark. So yes, definately a degree of familiarity there no doubt.