Here is my humble opinion.
The answer seems to be hidden in the question. For by asking "why" we pressuppose the existence of reason and hence a reasoner (God) prior to that of the world (universe).
To find out whether anything without God is possible, we first need to find out whether an explanation of the world without God is possible, and start with the question "How does the world exist?" not "Why does the world exist?".
Only after finding a satisfactory answer to this question can we find out if any kind of immortality is possible. And such an answer, we do not yet possess.
Therefore, my humble response is: we do not yet know how to have immortality without God.
When we find out how and achieve it we might have self sufficient advanced robots by then who might refer to us as immortals.
Yea, who knows, after all, history might repeat itself. :D

