The only "clue" I have is the Christian god creating the world in seven days, but I don't really think they invented the idea. Who came up with weeks, who liked 7 days?
I've always wondered "why 7?" 364 is a multiple of 7, so the year is almost perfectly divided, but dividing by 7 isn't very nice. 5 day weeks would be a better division (though you will always have the leap year issue).
Were there ever cultures with a concept of weeks that weren't seven days?
The idea of a seven-day week is grounded in the lunar cycle since four weeks is roughly equal to a lunar cycle. Alexander Marshack (1918-2004) in his controversial 1972 book, The Roots of Civilization maintained that he consistently found scratch marks in Upper Paleolithic art that revealed patterns of 7, 14, and 28. Although he may have overstated the case, at least some of his examples are persuasive, suggesting that a seven-day cycle may be extremely old.
The following is an excerpt from my Introduction to Folklore, addressing some of the issues around the history of the week:
People throughout the world recognize a period of time ranging from three to ten days that plays the same role as the modern week. These are frequently divisions of the lunar cycle. In agricultural societies, the week is often four to five days and is tied to markets. Central Africa, for example, has a four-day week with the market as the focus.
For the Babylonians, seven was a particularly important number. They recognized seven heavenly bodies that moved independently of the stars: what we now call Mercury, Venus, Mars, Jupiter, Saturn, the sun, and the moon. Each of these astronomical objects corresponded to a deity. In addition, much of Babylonian astrology focused on the moon, each phase of which lasts approximately seven days. It was easy, therefore, to associate each day of the week with a deity. The Romans, adopting this practice, began the week with Saturday, naming that day for Saturn, the most remote and slowest of the visible moving planets. Days for the sun and moon followed, and then Mars, Mercury, Jupiter, and Venus had their respective days. Romance languages preserve these pagan designations.
The Germanic world imported the Roman concept of the week before Christianization, so they substituted the names of their own gods for the Roman ones. They only had, however, a four-day week, and they consequently discarded Saturday through Monday, which returned later with the Christian faith. In addition, the Germanic world did not associate celestial objects with their gods, and as a result, the designations for the days of the week had no counterpart in astrology.
Tiw/Týr, the god of war, assumed the position of Mars. Odin, god of wisdom and magic (Woden for the Anglo-Saxons), took the place of Mercury, although in both cases the analogy was weak. Thor, the Germanic sky god of thunder, was a more obvious substitute for Jupiter. Freya, goddess of love and fertility, assumed the place of Venus.
The preoccupation of the Christian calendar with the importance of Sunday as that religion’s Sabbath was influenced by the popularity of a Roman religion known as Mithraism, which held the sun as sacred. For the Germanic world, Thor was generally regarded as supreme, and so Thursday assumed premier significance. The important role of Thursday, as opposed to Sunday, created an ambiguity for Northern European folk culture until industrialization and the adoption of the idea of a weekend, consecrating Sunday as the Sabbath. In Germanic-based European folklore, the evening before Thursday or Sunday were the best time for magic. In addition, dreams during those nights had greater potential to become reality. A person born on Thursday should not be baptized on Sunday, and the opposite was also true. If this taboo were broken, the child would grow up seeing ghosts. In addition, only those born on one of those two days had the potential to become a sorcerer.
The Chinese used to split each month into three "weeks" known as 旬 ("xún") that generally consisted of 10 days. This was based on the lunar cycle
The first two were known as 上旬 (upper week, pronounced "shàng xún") and 中旬 (middle week, pronounced "zhōng xún"), both consisting of 10 days. The last one was known as 下旬 (lower week, pronounced "xià xún") and consisted of all the remaining days in the month
/u/nortti_ talks about a few others here too
Follow-up: Do we have any evidence of the observance of a weekly-ish day of rest in ancient Mesopotamia or the Levant that predates the redaction of the Torah? I have trouble understanding how, by itself, the appearance of a document in a politically tumultuous region could spread around a custom like the Sabbath.