1) did the nephilim exist?
Sure.
The Biblical Nephilim were merely tribes of people who were unusually tall from the point of view of the Biblical authors.
There are tribes of people living today who have that same characteristic (being unusually tall, even from our fairly tall perspective).
2) they are mentioned in biblical scriptures. large beings who were born from human women and fallen angels.
That is NOT how the Bible describes them.
Even if you interpret the phrase "sons of God" as "fallen angels"
- that would be a real stretch, but let's pretend it's OK
the Bible teaches us that the Nephilim existed BEFORE the "sons of God" produced children by human women.
https://www.biblegateway.com/passage/?search=gen+6%3A4&version=NASB;NRSV