What is the oldest historical evidence of the Sabbath commandment? What does history say about the practice of keeping the Sabbath holy? What is the oldest historical evidence of this commandment? Can we find evidence of Sabbath keeping prior to the Israelites and/or in other cultures?
At the very latest, in Babylonia, which is where exiles from the Kingdom of Judah picked up their own month names as well.

By &quot;in other cultures,&quot; I'll take this to mean that you're looking for non-Judeo-Christian answers.
And first off, let's define what we mean by &quot;prior to the Israelites.&quot; Per Encyclopedia Britannica:

The earliest record of the reading of a “Torah book” is provided by the narrative describing the reformation instituted by King Josiah of Judah in 622 BCE following the fortuitous discovery of a “book of the Torah” during the renovation of the Temple.

That's our starting point.
Sumeria (~2600-2100 BC?)

[...] there is every probability that [the Hebrew Sabbath] had its origins in Babylonia. In that country, however, it was not the rest-day ending the seven-day week [...] but was due to the festival of the full moon on the 15th day of the month, when the earth's satellite 'rested' for a while at the height of his brilliancy. [...] The word by which the Babylonian Sabbath is designated is the somewhat rare term sappatu or sabbatu [...] u-hut-allum, from the Sumerian u-hul-gala, which they translated by umu limnu, &quot;evil day[,]&quot; [was] the 7th, 14th, 21st, and 28th days of every month, so that, as the Babylonian months had 29 or 30 days each, every month consisted of seven days each, and one of nine or ten days, according to the length of the month. [...] The following is a paragraph given by hemerologies for the observance of the seventh day of the month as a sabbath:

The 7th day is a holy-day (nubattu) of Merodach and Zer-panitu--an acceptable day, an evil day (u-hulgallu). The shepherd of the great tribes (nisi rabati) shall not eat salted meat cooked over the embers, he shall not change his body-clothing, eh shall not be clothed in white, he shall not offer a sacrifice. The king shall not ride in a chariot, he shall not talk victoriously. The seer shall not make a declaration with regard to a sacred place. A physician shall not touch a sick man. It is not suitable to make a wish.


Source: Encyclopedia of Religion and Ethics, James Hastings, ed.,  page 889-890 of the book/912 of the scan. Forgive me, as there are many accents on the Akkadian(?) words there that I am not able to easily reproduce. (Note: Source is from 1918.)
To me, that last bit sounds strikingly like an Orthodox Jewish Sabbath.
However, I'm wildly unsure of the year here. Wikipedia calls the Babylonian calendar a successor to a 21st century BC Sumerian calendar. The Sumerians were definitely into sevens (source page 1, source page 2):

The Sumerians not only regarded seven as the perfect number, but even recognized seven-day periods, prototypes of the week. As early as 2600 B.C. Gudea, able priest-king of Lagash, built a seven-roomed tower temple and dedicated it with a seven-day festival. [...] Seven-day periods are mentioned also in the Assyro-Babylonian epic of Gilgamish, whose origins go back to the third millennium B.C., or to Sumerian times. [...]

The source then goes on to describe the 7th, 14th, etc. days as evil days, as previously mentioned.
Deir el-Medina, ancient Egypt, ~1550-1080 BC
(Estimated years from Wikipedia)
The Egyptians constructed their year into months of three ten-day periods called decades, plus a five-day intercalary month.

A reconstruction of a festival calendar of Deir el-Medina, however, has been  compiled by Wolfgang Helck by utilizing references to working and inactivity in the  administrative documents pertaining to the royal artisans’ community. [...] Helck  collated  the references to  working  and inactivity into  tables  and,  by  analysing these, he was able to conclude that the ninth and tenth days of a decade were ‘as a  rule’  work-free.

Source, page 39 of the paper/45 of the PDF. The source then lists 17 feasts that would have also been work-free.
However, I'm not sure that this really counts, as I don't see a reference to keeping the 9th and 10th days holy per se.
Assyro-Babylonia, 7th century B.C.
In any case, it seems pretty widely-accepted that the Jewish calendar got their month names after the period of Jewish exile in Babylon (source). Here's part of the text of a &quot;Assyro-Babylonian epic of creation,&quot; which includes Sumerian material (quoted here).

Then Marduk assigned to the moon god
Control of the night and said:
'Each month your tiara of beauty
Shall shine on the evening's head.
For you shall measure the cycles;
Six days you shall show horns of light;
The seventh your crown shall be finished;
The fourteenth both halves shall be bright.