A.B. Davidson puts it like this:

Man so far as we can gather from the narrative in Genesis, was made neither mortal nor immortal. He was not made so that he must die, for the narrative represents him surrounded by the means of living for ever; nor was he so made that he could not die, for the event has too clearly shown the reverse. He was made capable of not dying, with the design that by a free determination of his activity rewarded by God’s favour, he should become not capable of dying.¹

Here’s my proposal: I would suggest that the Bible teaches that God alone is intrinsically immortal, but He can bestow his immortality upon others. This He did at creation, making man as a holistic-dualistic entity: a physical body created mortal, into which he breathed a soul, possessing something of His own immortality. Man was placed in the Garden of Eden, with the option to eat from any tree, including the Tree of Life and the Tree of the Knowledge of Good and Evil. The former was permitted, and would have resulted in his mortal flesh being made immortal, and thus he would achieve the consummation without having to undergo the pain of dichotomy through death. The latter was prohibited, and the punishment for disobedience was the unnatural experience of separation of body and soul.

Upon eating of the forbidden tree, man was restricted from taking of the Tree of Life, lest sin become immortally consummated. Immortality was not, therefore, revoked, though its possibility was removed.

Now unable to eat from the Tree of Life, death as separation of body and soul is the inescapable fate of man. “To use the classical distinctions, man was not created unable to die (non posse mori) but able not to die (posse non mori), although after the Fall he was unable not to die (non posse non mori).”²

Today, the soul remains immortal, whilst the body remains mortal and corrodes. Yet through the gospel, Jesus allows another chance for man to receive the consummation at the resurrection of the dead, when the body and soul will be reunited and transformed as a whole, into the immortal holistic unit we were always intended to become.

So, when might a believer be said to gain immortality? I conclude with this helpful quote from Murray J. Harris,

The only unambiguous testimony places the receipt at the time of resurrection, be that at the individual believer’s death or on the last day, although one passage (1 Pet 1.23) could be taken as linking immortality with regeneration […] We may reconcile the two positions by saying that the seed of immortality is implanted by regeneration but the full flower appears only after resurrection, with the New Testament emphasis falling almost exclusively on the second stage of final maturation […] immortality gained potentially at the moment a person comes to be in Christ (cf. 1 Cor 15.22b; 2 Cor 5:17) becomes an actual possession in the resurrection of the dead.³