1) While the traditional understanding is that Yosef was sold after Rachel's death, I would suggest that in fact he was sold before Rachel's death.
2) If Rachel died before Yosef was sold, then Binyamin would be at least 23 when he the brothers stood before Yosef. Yosef was sold at 17, stood [before Pharaoh when he was 30, and the brothers] stood before him when he was 39 [
3) How can this be? After all, Rachel died on the way back from Padan Aram on the way home. Yet Vayeishev, which describes the selling of Yosef, begins that Yaakov settled in the land of his father's sojournings. The answer is that this first pasuk is unrelated to the narrative that follows. This first pasuk really belongs to the previous parsha, and is there to match the statement that Esav settled in Seir.
4) If Binyamin is so young, how could he have 10 children (see 46:21) who came down to Egypt (listed among the 70)? It is difficult enough if he is between 22 and 30, but now he is a mere youngster?
Even without making Binyamin younger and redefining the chronology, it is difficult for Binyamin to have had all these children in such a short time span.
The same is true for Yehuda's children and grandchildren. Wer have a relatively short timespan (even if we make Yehuda leave his brothers and marry his first wife Bet Shua before Yosef is sold). In that short timespan, Yehuda needs to marry his first wife, have three children, have them grow up sufficiently for the first two to marry Tamar and die, for Yehuda to sleep with Tamar and have the twins, and also for Peretz, one of the two, to grow up sufficiently to marry and have two children, Chetzron and Chamul (see 46:12), grandchildren of Yehuda who are listed among those coming down to Egpyt.
There is also the difficulty of Reuven's children, who seem to be tribbles, in that they double suddenly. If promising Binyamin's safe return, Reuven tries to put up the lives of his two children. Yet in (46:9) Reuven has four children: Chanoch, Pallu, Chetzron and Karmi.
I'll put forth another question. How could Ephraim and Menashe be among the count of 70 that came down to Egypt, when the same verse states they were born in Egypt (46:27)?
5) My answer to this is that in (46:27), the phrase כָּל-הַנֶּפֶשׁ לְבֵית-יַעֲקֹב הַבָּאָה מִצְרַיְמָה and in the previous verse, the phrase כָּל-הַנֶּפֶשׁ הַבָּאָה לְיַעֲקֹב מִצְרַיְמָה, does not mean that they physically entered the gates of Egypt (Ephraim and Menashe being the best proof of this).
Rather, there was a generation that entered Egypt. As opposed to the generation that left Egypt. But this does not mean they physically passed through Egypt's gates. Rather, this first generation, the founding generation in Egypt, deserves a census at some point. This could have been taken much later, say at the time of Yaakov's death.
If so, Binyamin, Yehuda's sons, and Reuven have plenty of time to have more sons. And so Binyamin can indeed be very young.
6) Because Meir was asking me to read to him Curious George Goes to the Beach once again, I neglected to mention some of the more interesting evidence.
The brothers envy their father's love for Yosef, which is due to Yosef's being a ben zekunim. No mention is made of Binyamin, who is even more of a ben zekunim, and who is referred to by Yehuda later as a yeled zekunim.
The brothers are grazing in Shechem, and we know that the incident involving Dinah in Shechem took place before Rachel's death.
Yaakov says to Yosef's second dream, "shall I, your mother, and your brothers..." The midrash takes off on this, saying that Yaakov is saying that the dream is impossible because Rachel is dead, not knowing that Bilhah was being referred to. On a peshat level, it would seem that Rachel is still alive when Yaakov says this.
That Yosef sees 11 stars - this might be taken to refer to Dinah, at least is unremarked upon in the story, even if it eventually turns out to be Binyamin. Yaakov just says "your brothers," not "your 11 brothers."
Yes, it involves some level of ain muqdam ume`uchar batorah, but this is necessary in the case of stories that extend past a long timespan, and genealogical details such as Rachel's death and Binyamin's birth are exactly where we this stepping out of the bounds of straightforward chronology (see my other posts about this).