Homo Sapiens - Is There an Immortality in the Human Family Tree?

Homo sapiens appeared approximately 300,000 years ago. And is there any way to know when God imbued man with an immortal soul that will transcend physical death? It's always seemed arbitrary to me where a distinction would be made in the evolutionary process of mankind as to when an immortal soul would be present. This is, of course, simplified by the Adam and Eve creation narrative.