Adam and Eve did not have that and they were fully human.
Incarnation is a mystery, not ordinary conception. There is nothing that necessitates or justifies any speculation as regards to that miracle. Least of all claiming that Mary's egg was somehow "fertilized." Fertilized ovum is a separate individual. C hrist was one and the same Divine Person, Logos, before and after.
I see that the question of Christ's genetics has again come up downthread.
The words "made like us in all things, excepting sin" in one of the prayers in the Divine Liturgy for Theophany, struck me as relevant to our discussions. Just as the Fathers, doubtless had in mind the noetic intelligences as the 'invisible', when they included "maker of all things visible and invisible" in the Creed, but wisely did not say 'material and noetic', but 'visible and invisible', thereby affirming for us in these latter days that the Father made quarks, gamma rays, the curvature of space-time, and a host of other invisible things that are not part of the noetic realm, so I would not discount the Church's perceptiveness in praying down the centuries "made like us in all things, excepting sin" to assert that Christ's body (or Adam and Eve's bodies) did not include instructions encoded in DNA--not inherited in an ordinary conception, but there, nonethless--describing the enzymes by which Christ in His humanity digested ordinary earthly food, describing the proteins of the muscles which carried the Cross, the nerves that bore the material portion of His agony in His Passion and Saving Death, and the like. To assert otherwise is either to deny the doctrine contained in the prayers of the Church, or to assert that having bodies with instructions encoded in DNA is somehow in itself sin, a very strange position, indeed.
I agree that there is no point in speculating as to the material means of the Virgin's conception, though these seem to me closer to human comprehension than the far deeper mystery of the Hypostatic Union.