The Talmud at Bava Basra 14b-15b teaches that Moses wrote the Book of Job before the Exodus. If so, was he a contemporary and a witness to Job's suffering, was he describing a historical figure he didn't know, or was it simply an inspirational fable?
There are many different opinions regarding when Iyov existed, if at all. Many are mentioned in the Talmud you cited in your question.
The Talmud (Sotah 35A) brings an opinion that Iyov died shortly before the spied entered the land, a little more than a year after the Jews left Egypt.
The Talmud (Babba Batra 15A) (translation here) says that Moshe told the spies to see if Iyov was in the land.
The Talmud there also brings an opinion that 'The span of Job's life was from the time that Israel entered Egypt till they left it.'
According to Iyov 42:16, Iyov lived 140 years after his suffering. Since Moshe was only 80 at the time of the Exodus, he would not have seen Iyov's suffering.
Basically there are multiple valid opinions.
Various midrashim put him roughly around the same period as Moshe (though Sforno reads that "Utz", a nephew of Avraham's, is in fact "the man from the land of Utz" i.e. Iyov). There's another opinion that the story is in fact fiction, "Iyov never existed and never was created."