What is the oldest historical evidence of the Sabbath commandment?

The early christian gentile apostolic churches did not keepany sabbath.

Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross; and having spoiled principalities and powers, he made a shew of them openly, triumphing over them in it. Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath days: Which are a shadow of things to come; but the body is of Christ. Colossians 2:14-17

The Sabbath is mentioned at the beginning of the creation [thus]: "And God made in six days the works of His hands, and made an end on the seventh day, and rested on it, and sanctified it." Attend, my children, to the meaning of this expression, "He finished in six days." This implies that the Lord will finish all things in six thousand years, for a day is with Him a thousand years. And He Himself testifies, saying, "Behold, to-day will be as a thousand years." Therefore, my children, in six days, that is, in six thousand years, all things will be finished. "And He rested on the seventh day." This means: when His Son, coming [again], shall destroy the time of the wicked man, and judge the ungodly, and change the sun, and the moon, and the stars, then shall He truly rest on the seventh day. Moreover, He says, "You shall sanctify it with pure hands and a pure heart." If, therefore, any one can now sanctify the day which God has sanctified, except he is pure in heart in all things, we are deceived. Behold, therefore: certainly then one properly resting sanctifies it, when we ourselves, having received the promise, wickedness no longer existing, and all things having been made new by the Lord, shall be able to work righteousness. Then we shall be able to sanctify it, having been first sanctified ourselves. Barnabas (A.D. 70-130) ch. 15

Further, He says to them, "Your new moons and your Sabbath I cannot endure." You perceive how He speaks: Your present Sabbaths are not acceptable to Me, but that is which I have made, [namely this,] when, giving rest to all things, I shall make a beginning of the eighth day, that is, a beginning of another world. Wherefore, also, we keep the eighth day (Sunday) with joyfulness, the day also on which Jesus rose again from the dead. And when He had manifested Himself, He ascended into the heavens. Barnabas (A.D. 70-130) ch.15

If then those who had walked in ancient practices attained unto newness of hope, no longer observing Sabbaths but fashioning their lives after the Lord's day, on which our life also arose through Him and through His death which some men deny. Ignatius: to the Magnesians (A.D. 35-105) ch.9

But again their scruples concerning meats, and their superstition relating to the Sabbath and the vanity of their circumcision and the dissimulation of their fasting and new moons, I do [not] suppose you need to learn from me, are ridiculous and unworthy of any consideration… And again to lie against God, as if He forbad us to do any good thing on the Sabbath day, is not this profane? Letter to Diognetus (A.D. 125-200) ch. 4

The new law requires you to keep perpetual Sabbath, and you, because you are idle for one day, suppose you are pious, not discerning why this has been commanded you: and if you eat unleavened bread, you say the will of God has been fulfilled. The Lord our God does not take pleasure in such observances: if there is any perjured person or a thief among you, let him cease to be so; if any adulterer, let him repent; then he has kept the sweet and true Sabbaths of God. If any one has impure hands, let him wash and be pure. Justin Martyr (A.D. 160) Ante-Nicene Fathers vol.1 pg.200

Do you see that the elements are not idle, and keep no Sabbaths? Remain as you were born. For if there was no need of circumcision before Abraham, or of the observance of Sabbaths, of feasts and sacrifices, before Moses; no more need is there of them now. Justin Martyr (A.D. 160) Ante-Nicene Fathers vol.1 pg.206

"You hypocrites, does not each one of you on the Sabbath-days loose his ox or his ass, and lead him away to watering? And ought not this woman, being a daughter of Abraham, whom Satan has bound these eighteen years, be loosed from this bond on the Sabbath-days?" It is clear therefore, that He loosed and vivified those who believe in Him as Abraham did, doing nothing contrary to the law when He healed upon the Sabbath-day. For the law did not prohibit men from being healed upon the Sabbaths; [on the contrary,] it even circumcised them upon that day, and gave command that the offices should be performed by the priests for the people; yea, it did not disallow the healing even of dumb animals. Both at Siloam and on frequent subsequent occasions, did He perform cures upon the Sabbath; and for this reason many used to resort to Him on the Sabbath-days. For the law commanded them to abstain from every servile work, that is, from all grasping after wealth which is procured by trading and by other worldly business; but it exhorted them to attend to the exercises of the soul, which consist in reflection, and to addresses of a beneficial kind for their neighbors’ benefit. And therefore the Lord reproved those who unjustly blamed Him for having healed upon the Sabbath-days. For He did not make void, but fulfilled the law, by performing the offices of the high priest, propitiating God for men, and cleansing the lepers, healing the sick, and Himself suffering death, that exiled man might go forth from condemnation, and might return without fear to his own inheritance. Irenaeus (A.D. 180) Ante-Nicene Fathers vol.1 pg. 471

To His disciples He said, who had a priesthood of the Lord, to whom it was lawful when hungry to eat the ears of corn, "For the workman is worthy of his meat." And the priests in the temple profaned the Sabbath, and were blameless. Wherefore, then, were they blameless? Because when in the temple they were not engaged in secular affairs, but in the service of the Lord, fulfilling the law, but not going beyond it, as that man did, who of his own accord carded dry wood into the camp of God, and was justly stoned to death. Irenaeus (A.D. 180) Ante-Nicene Fathers vol.1 pg.471

And in Exodus, God says to Moses: "And you shall observe My Sabbaths; for it shall be a sign between Me and you for your generations."… But the Sabbaths taught that we should continue day by day in God's service. "For we have been counted," says the Apostle Paul, "all the day long as sheep for the slaughter;" that is, consecrated [to God], and ministering continually to our faith, and persevering in it, and abstaining from all avarice, and not acquiring or possessing treasures upon earth. Irenaeus (A.D. 180) Ante-Nicene Fathers vol.1 pg. 481

It follows, accordingly, that, in so far as the abolition of carnal circumcision and of the old law is demonstrated as having been consummated at its specific times, so also the observance of the Sabbath is demonstrated to have been temporary. … And through this arises the question for us, what Sabbath God willed us to keep? For the Scriptures point to a Sabbath eternal and a Sabbath temporal. For Isaiah the prophet says, "Your Sabbaths my soul hates;" and in another place he says, "My Sabbaths you have profaned." Whence we discern that the temporal Sabbath is human, and the eternal Sabbath is accounted divine. Tertullian (A.D. 198) Ante-Nicene Fathers vol.3 pg.155

Theories finding Babylonian origins for the Sabbath have fallen out of favor. See William W. Hallo, "New Moons and Sabbaths: A Case-study in the Contrastive Approach", Hebrew Union College Annual 48,1-18(1977). The Babylonian calendar was entirely oriented to the phases of the moon. The Israelite sabbath, all the evidence tells us, had nothing to do with the phases of the moon.

The Sabbath is pre exilic, for it it mentioned by the prophet Amos:

Hear this, you who trample upon the needy and bring the poor of the land to an end, saying "When will the new moon be over, that we may sell grain? And the sabbath,, that we may offer wheat for sale? (8.4-5)

This presupposes that there was no buying or selling on the sabbath.

Proof that the sabbath was a continuous 7-day cycle is found for the exilic period in the Book of the Prophet Ezekiel:

Thus says the Lord God: The gate of the inner court that faces east shall be shut on the six working days; but on the sabbath day it shall be opened and on the day of the new moon it shall be opened. (46.1)

The simplest conclusion is that the pre-exilic sabbath was a continuous 7-day round also.

At the very latest, in Babylonia, which is where exiles from the Kingdom of Judah picked up their own month names as well.

By "in other cultures," 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 "prior to the Israelites." 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, "evil day[,]" [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 "Assyro-Babylonian epic of creation," 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.