Yep, the Word has always been true. Always.
But what you quoted was NOT the WORD as in Genesis 3:15. Eve was the mother of all living (Christ is the tree of life eternal) in that she was the beginning of the lineage, even to Mary of Christ. Mary would not have been where she was appointed to be had it not been for Eve. Regardless of Eve's sin, Christ still came through her lineage. And if any or one is tainted by Eve's sin so would Mary...
It takes numerous 'new' cuts on Peter's keys to get to claiming Genesis 3:15 is speaking about Mary.