The answer to this question is yes. Not only is it possible, but it happened in time and space. Neo-orthodox theologians (twentieth-century thinkers strongly influenced by Karl Barth) have said that the question is logically unanswerable because faith is an illogical paradox and can be seen only through the eyes of faith. In recent years liberal theologians have denied the reality of the incarnation on the grounds that it is a myth and not true in any objective sense. In the nineteenth century advocates of kenotic Christology (emphasizing the “emptying” of Christ in keeping with Php 2:7) argued that in the incarnation the divine Logos (Word) suspended the characteristics of deity because they were in principle incompatible with human attributes, thus making nonsense of the claim that Jesus Christ was fully God and fully man (as both the Bible and historic Christian confessions have claimed).
Historical, Bible-based theology has argued that God is omniscient (all knowing), omnipotent (all powerful), sinless, and incorporeal (without a body) and that these attributes are essential and necessary to deity. Characteristically, human beings do not exhibit these attributes. So how can Jesus simultaneously be fully divine and fully human? Along these lines, people have attacked the doctrine of the incarnation, claiming that it is illogical and contradictory.
Ronald Nash summarizes the implications of the argument as follows:
This means two things: Jesus possesses all the properties that are essential to being a human being, and Jesus possesses all the properties that are essential to deity. The historic understanding of the Incarnation expresses the beliefs that Jesus Christ is fully God—that is, He possesses all the essential properties of God: Jesus Christ is also fully human—that is, He possesses all the essential properties of a human being, none of which turn out to be limiting properties: and Jesus Christ was not merely human—that is, he did not possess any of the limiting properties that are complements of the divine attributes. In the face of these distinctions, the alleged contra- diction in the Incarnation disappears.