Can it be "the men" too?

Hmm, it sounds odd in English. No comment about how it would sound in French.

In French it sounds awkward. Better" Les hommes ont mangé avec leurs doigts depuis le commencement des temps"
In effect, I can't see this as being "History" since history is a written record, and we have no written record as to when humans started eating with their fingers. Before, it is pre-history.
That is why I recommend "since the beginning of Times".

or "...depuis la nuit des temps." if we want to insist that they did from the beginning, although we don't know if they didn't eat with their toes or just plain teeth before...

I am afraid I did something wrong: I cut the link with the Esperanto version, because I thought it was also linked to the English...

Si I suggest something along: "Man has eaten with his fingers since the beginning of times" if that matches Japanese...

I fixed your link (assuming you wanted it to link to the English).