After taking a course on early civilizations, it seemed as though Judaism (later Christianity) was heavily influenced by other forgotten religions - so how original was Judaism from a historical perspective and which components can really be traced to being borrowed from other cultures?

Modern commentaries on the book of Genesis have taken into account a lot of the newly discovered archaeological evidence of other ancient Near Eastern (ANE) civilizations, especially their religious beliefs about the creation of humankind. To get started you could check out Cassuto (Jewish) or Wenham (Christian) who both have some well-respected Genesis commentaries published.

It is interesting to see so many parallels between the Jewish creation story and others in the ANE. There is a general consensus that the Jewish narrative was meant to contrast with these other belief systems, showing a picture of a God who is more powerful and sovereign, as well as humankind being created with a purpose more intimate with the rest of the creation. For example, ANE gods are often portrayed creating people from the mud like a potter, even breathing life into them (all imagery present in Genesis), but those gods typically created people to do jobs that the gods didn't want or couldn't do on their own. In contrast, Genesis shows a God that created people, not out of any type of shortcoming or need, but to share in the creative process (e.g., Adam naming animals in Gen 2), and to join God in caring for creation. The "fall" of humanity in Gen 3 is also a unique aspect of the Jewish tradition, so there is definitely more unique than similar to other ANE religions. That seems to be the point though... Genesis was likely written (there's not consensus) during the time of Israel wandering the wilderness, hoping for the promised land, and constantly falling back into worshipping the gods of the surrounding cultures. There's obviously a lot more that could be said here... it really requires some dedicated research.

To address some possible side issues or questions... The fairly recent approach of theologians treating Genesis like a history book is quite misaligned with the text in many ways. Genesis doesn't claim to be the first creation account, and it's probably not even the earliest text within the Jewish scriptures. It does, however, claim to speak about a God who stands above other gods and belief systems; this seems to be the main point of the book, and when seriously considered it proves a more challenging and insightful text about the nature of God and humanity.