Considering the origins of the tenet of marriage, to be fruitful and multiply, the bride is given in marriage, that is she gives herself to the groom, who offers his seed. Does the seed represent faith? I don't believe so as it seems rather that it represents the word of truth and the seed of woman, the ovum, receives it so it would fit the representation of faith much better. And at this point, the new child is created, i.e. the new creation.
Now, the ovum is of the woman as much as it is instrumental in forming the substance of the new creation, but not without the substance of the seed as, if the seed is rejected, there is no new creation.
So, was the capability always there in those that are never born again? Some have answered no.
However, keeping in mind spiritual birth is different from natural birth in that it most likely resembles Jesus' birth rather than Adam's as much as any subsequent births after the creation of Eve, where Jesus is from the Father so are those born of the Spirit. But even Mary said, when Gabriel announced God's intentions, "Be it unto me..."