Following up on this question, this Sabbath I happened to read in Israel Knohl’s book (published in 2018), How the Bible Was Born, where he writes as follows:

“There is a gap of many hundreds of years between the time when the initial core of the Genesis stories was created and the writing down of the stories in a process that began in a relatively late period, from the eighth century BCE onward. Therefore there is quite a bit of anachronism in the stories. These stories also contain names and descriptions of facts that could not have existed in the settlement period or before the settlement period. Such as the domestication of the camel … the camel was not domesticated before the tenth century BCE, and research recently conducted at Wadi Faynan, in the region of the copper mines at Punon, east of the Jordan, has once again confirmed the fact that there were no domesticated camels before the tenth century.”

I also saw on Wikipedia that it says this:
Recent excavations in the Timna Valley by Lidar Sapir-Hen and Erez Ben-Yosef discovered what may be the earliest domestic camel bones yet found in Israel or even outside the Arabian Peninsula, dating to around 930 BC. This garnered considerable media coverage, as it is strong evidence that the stories of Abraham, Jacob, Esau, and Joseph were written after this time.

That is, despite there being dissenting views, the most up-to-date studies show evidence that the camel, at least in the Middle East region, was domesticated after the time of the patriarchs.

Rabbi Amnon Bazak writes in his book Until This Day (pp. 260–263) that a document was found from Alalakh in northern Syria, dated to the 17th century BCE, in which it says, “one ration of food for a camel”; in excavations at a site in the Negev highlands (Be’er Resisim) from the end of the third millennium BCE, camel bones were found together with goat bones; and in addition, he writes: “There is evidence of early camel domestication, from the fourth millennium BCE in the deserts of Iran, and in other places as well.”
On the other hand, he writes:
“The abundance of archaeological finds concerning camels from the 12th century BCE onward indicates that the camel suddenly became much more widespread. This finding essentially corresponds to what is stated in the Bible, since until the period of the Judges, camels are mentioned only a small number of times, and even when they are mentioned their numbers are low (‘ten camels of his master’s camels,’ ‘milch camels and their colts, thirty’)… From the period of the Judges onward, a large number of camels appears (‘and they took away their livestock, their camels, fifty thousand’).” Rabbi Bazak is basically showing that in this case there is a correspondence between the Bible and archaeology, since the level of camel domestication and its change over time as described in the Bible corresponds fairly well to the level of camel domestication and its change over time that emerges from the archaeological finds.
Nadav Na’aman, Israel Finkelstein (and Silberman), and Israel Knohl still argue that there is an anachronism. As I understand it, the reason is that in their view Genesis still refers to a level of camel domestication greater than what would be expected.
In any case, Professor Kitchen (emeritus professor at the University of Liverpool, and highly regarded) wrote, regarding the approach of Finkelstein and Silberman: “With regard to the patriarchal period and the Exodus, our two friends are entirely lacking in depth, hopelessly mistaken, and thoroughly misleading… Camels are not an anachronism in the early second millennium, and never were.”

The seam here is very fine.
In my humble opinion, Rabbi Bazak brings examples that show that the animal—the camel—existed then, more than that it was used for travel and the like. So perhaps it is still difficult to explain how the book of Genesis describes journeys. On the other hand, if in the future more early finds are discovered that could testify to such use already at that time, that would significantly weaken the anachronism claim. Is it even likely that such a thing will be found? Either way, the very disproportionality in the findings points to the estimated level of domestication in the different periods… perhaps the researchers allowed themselves to assume that there is an anachronism because in their eyes the book of Genesis somewhat exaggerates.
In any case, it is hard to decide.

With God’s help, 25 Elul 5782

The difference in the level of camel domestication between the periods stands out in the fact that in the spoils of Midian in Moses’ time there are no camels at all, whereas in Gideon’s time there are tens of thousands of camels in Midian’s camp.

In the days of the patriarchs, camels were used only for international trade, and only exceptional individuals, major merchants, kept the “ship of the desert” in their possession. Abraham’s servant sets out on a long journey with camels, meant also to impress his relatives in Haran so that they understand that “they’re dealing with” an enormously wealthy man. The transporters of luxury goods too—”gum tragacanth, balm, and ladanum from the east to Egypt”—use the prestigious “ship of the desert.” Not just any common folk.

Best regards, Nehorai Shraga Agami-Pesisovitz

Jacob is initially careful not to arouse Esau’s jealousy, and at first speaks only of “ox and donkey, flock, male servant and female servant.” Only when he sees that Esau persists in his hatred does Jacob bring out the camels and offer some of them as a gift to appease his brother.