I think that there is something worth adding to the answer given by @RoToRa, particularly as you ask for a literal translation into English.
I think that a close rendition into English — rather than a word-by-word attempt — must (i) deal with the words Allesfresser Mensch that you specifically asked about, and (ii) correctly capture the Konjunktiv II form of the second part of the sentence (which you didn't mention and which isn't properly captured in the answer of @RoToRa )
As, so often with language, the choices that one has in translation are often constrained by context, but they are sometimes expanded by the context because it gives one an opportunity to rely on what the speaker already knows. The sentence fragment that you quote appears, slightly changed, in the Aspekte Neu B2 Lehrbuch where the context is as follows :
Bis heute weiss die Wissenschaft nicht, warum der Mensch ein Drittel seines Lebens verschläft. Damit die Organe entspannen? Oder weil die Erde kahl wäre, gäbe der Allesfresser Mensch nicht zwischendurch Ruhe?
A close translation might be:
To this day, science does not know why humans slept away a third of their lives. To allow the body to recuperate? Or because the earth would be bare were the omnivores not to give it occasional rest.
Clearly this differs from any kind of word-for-word approach to the German sentence but I do think that it gives a more "complete understanding" (at least to a native English speaker) of what is being said in the German. Specific points:
I think that Allesfresser Mensch is better rendered in the context simply as omnivores. It is obvious that we are talking about humans. So, although the German could be rendered as ominvore humans (compound-noun and not humankind), or more likely, omnivorous humans (adjective noun), the word omnivores seems better.
... were the omnivores not to ... captures the Konjunktive II form of ... gäbe ... nicht ... .
... slept away a third ... is a better English rendition for verschläft than overslept. (Of course, in the quotation as you have given it, with the verb schlafen, ... slept a third ... would work just fine. The point about slept away is that it emphasizes the apparent waste.
One would be unlikely to read about resting "the organs" in an English translation; instead, unless there was specific evidence about how an organ such as the heart was affected by sleep, one would be more likely to read about "the body".
N.B. Thanks to Hubert Schölnast for highlighting an error in my terminology that detracted from the main point of my answer.