Well to add something more:
There are no specific written records explaining Mesopotamian religious cosmology that survive to us today. Nonetheless, modern scholars have examined various accounts, and created what is believed to be an at least partially accurate depiction of Mesopotamian cosmology, so we could not rush in such bold statments about that religion.
Concerning IE religions, giants exist in Scandinavian mythology and Greek, and story is essentially different.
Although it mostly died out 1600 to 1700 years ago, Mesopotamian religion has still had an influence on the modern world, predominantly because Biblical mythology that is today found in Judaism, Christianity, Islam and Mandeanism shares some overlapping consistency with ancient Mesopotamian myths, in particular the Creation Myth, the Garden of Eden, The Great Flood, Tower of Babel and Biblical characters such as Nimrod and Lilith (the Assyrian Lilitu). In addition the story of Moses' origins shares a similarity with that of Sargon of Akkad, and the Ten Commandments mirror Assyrian-Babylonian legal codes to some degree.
as far as i know these myths are some of the foundations of Christianity and Judaism, it's essential stories and they originate in mesopotamian religions which in turn derive from old Sumerian ones. Before these Babylonian and Sumerian myths there is no other Biblical myths, they're Abrahamic faith starts yet they are drawn from Mesopotamian religions. Too add Book of Enoch is as well derived from Babylonian/Sumerian religion. As far as Monotheism, it's just an evolution of following one polytheistic faith, as the main pantheon god becoming the supreme and most dominant one and turning from polytheistic into a monotheism faith, so mono/poly structure isn't really saying much especially when talking about happenings so old.
As for the IE religions and giants. Zeus fights his father Titan Cronos (his Creator) to imprison him so he could rule the world, while in Norse on example Odin kills giant Ymir to Create the world and rule it. However both have a similar Indo-European pattern of Gods fighting other high deities so they could rule. In Hindu Rig Veda it is Indra (equivalent of Thor, Perun etc.) that slays a high deity Vritra (dragon equivalent of Titan/Giant) so Indra could rule.
It could be but it doesn't have to mean IE faiths pre-date the happenings in Sumeria.