Since in light of modern science it's hard to take literally a description of 2 original humans alone in the world, here is how I understand the meaning of the Adam and Eve story.
Animals of a single species are essentially interchangeable with one another. As time passes some die and new ones take their place. But this transformation is of little significance; what matters is the species not individuals, and the species is effectively immortal. Within an animal's body cells continually die and are replaced by new cells; within a species animals die and are replaced by new animals. Both forms of death are insignificant, except from a biologist's perspective.
What is true of animals was also true of early humans, until they developed moral awareness. From the moment on, it was no longer possible to speak of individual humans as interchangeable, like cells in a body. Along with moral awareness comes a unique identity and personality - a soul. When a person dies, there is no identical, interchangeable person to take their place. Someone else takes their physical place, living in the same house, or working in the same profession. But morally speaking, this is a completely different person.
At the moment that he/she was tempted to eat from the Tree of Knowing Good and Evil, the immortal Adam - meaning Adam the species - ceased to be relevant. Adam the individual - and his children, their descendants, and all the other individual humans - became the focus of attention instead. Each of these people has their own unique identity, and each has a finite lifespan. The death introduced into the world by "knowledge of good and evil" was not physical death, but the death of moral identities. And the new sexuality which accompanies the "knowledge" is not the mating urge, which always existed, but rather the new ability to create new and unique moral identities.
Once Adam and Eve were confronted with the choice to obey or disobey, even before they chose wrongly, they had already made the transition from an immortal "species" to morally-aware "individuals". Had they chosen correctly, they would have stayed in the Garden as immortal individuals.
Such a state should not be so hard to imagine. It is well known and accepted that our inner identities - our souls - can themselves be immortal. Indeed we speak of them returning to the Garden of Eden, the place of immortality, after death. That is exactly what Adam and Eve would have achieved immediately had they not sinned.