I reply to myself to add a note, always from my personal notes – I'm almost surely wrong. Here[^1] it is quite well summed up: the Moon was only the beginning, the easiest phenomenon to observe. The fact that seven planets were "easily visible" with no astronomical tools surely helped, and in some civilizations the days were named along these.

Religions, finally, "officially" decided that a week had to have seven days.

[^1]: https://www.timeanddate.com/calendar/days/7-days-week.html