Your argument that the Nephilim came first after the sons of God had children is wrong. It is one sentence. The Nephilim were in the earth in those days when the sons of God came and had children with the daughters of men. If it was two sentences then you would be right, but it is just one.
If you are going to make an argument based on a verse, you ought to first quote it accurately. You left out a key phrase:
"There were giants on the earth in those days, and also afterward, when the sons of God came in to the daughters of men and they bore children to them. Those were the mighty men who were of old, men of renown" (Genesis 6:4).
The giants were on the earth before and also after the sons of God had relations with the daughters of men. The translation accurately reflects the Hebrew, even in the order of the phrasing. The fact that it is one sentence instead of two doesn't change the argument.