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I don't think that is what that verse meant. It says :
The Nephilim were on the earth in those days, and also afterward, when...
This was meant to explain how the Nephilim came to the earth. The when here explains how the Nephilims came :
the sons of God came in to the daughters of man and they bore children to them
So they were not there before but they came as a result of the union between those sons of God (fallen angels) and the daughters of men