The Nephilim were on the earth in those days–and also afterward–when the sons of God went to the daughters of men and had children by them. They were the heroes of old, men of renown.
-Genesis 6:4

How old is “old”?
Genesis 6:4 is a reference to a distant time when those “heroes” walked the earth.
We are actually reading about people from olden times in an account that is itself about the times of “old”. My point is, If Genesis itself is an account of a very distant past, then at exactly what time frame did these “heroes of old” exist?

One clue is that the starting of Genesis 6 implies a large amount of time had already passed since the creation of Adam.

“And it came to pass, when men began to multiply on the face of the earth, and daughters were born unto them.”

The Nephilim or the “heroes of old” came into existence only after human populations had increase on earth. This could mean a time gap of a few thousand years between the Nephilims arrival and the creation of man. Nothing is known about the events during the time frame when humans were multiplying on earth. The Genesis account is in no way a complete history of mankind. Genesis records a very, very tiny fraction of events that took place in the very early days of human history. It would be like trying to understand the entire history of the Chinese civilization from 2 or 3 lines. You may get a broad idea, but not the important.

When reading Genesis, its also very important to remember that writing was invented much after the arrival of man. (Historians estimate the date at around 3,200 BC) So the events of Genesis were preserved as oral traditions for thousands of years before being written down and a lot of it would have been forgotten over time. So all we have are blurry accounts of a faded memory of the distant past. How much of it has been lost over time?

Who were the “heroes of old”
With regard to this, there are many theories floating about and I believe all of them have some merit to them.

Some say the Nephilim were actually the Neanderthals. Their larger body structure and muscular build qualifies them to be the “heroes” of ancient mythology.

Or perhaps they were the humanoid “gods” of ancient civilizations. They would have been feared and respected by people and elevated to the status of “gods”.

Or perhaps they were those who became leaders of ancient civilizations. What did it take for one man or family during pre-historic times to assert themselves as being a “leader” over others? I’d say brute force or some ability that won peoples admiration.