I'm not sure we are a hybrid mix of the nephilim bloodline, my personal opinion is that the nephilim could not reproduce with humans, only themselves. A nephilim could be brought about by the union of a fallen one and a human female, but not a nephilim and a human female.

I also think that over time, through their own inbreeding the original "titanic" traits received through the fallen ones dissipated. That is why the Rephaim were described as smaller than the original titans of greek and roman mythology.

But I believe God was involved in our unique creation, as as such He imbued each one of us with a "soul" or something unique to us, our identity that could house the presence of the Holy Spirit, as when one is reborn that soul then becomes a spirit imbued by the Holy Spirit.

Ps 138:8 The LORD will accomplish what concerns me; Your lovingkindness, O LORD, is everlasting; Do not forsake the works of Your hands.