I don't get the "running out of fuel" argument... If the universe (as assumed in the text) is infinitely old and infinitely large, why should there be any scarcity of nuclear fuel?
I am not an astrophysicist, nor am I an expert in the early universe, but I recall that the prevailing theories of our time are that somehow the universe came in to being with predominantly hydrogen atoms. These combine through fusion in what we call stars to form denser matter. This process continues until the result of combining the elements reaches a limit. I believe that iron happens to be that limit if I recall correctly.
https://en.wikipedia.org/wiki/Iron_peak
Describes what I recall reading/hearing many years ago.