The sabbath was built into the framework of our reality. It's part and parcel of an earthly existence...the cycle of night and day constitute a day...every seventh one is the sabbath.
IT was set into motion at creation...Adam and Eve knew about it. Look at this verse:
Gen 4:3 And in the process of time it came to pass that Cain brought an offering of the fruit of the ground to the LORD.
"in the process of time" is literally "at the end of days". Many scholars believe this is a reference to the 7th day sabbath...the holy sabbath created earlier by the Lord Jesus Christ. The "end of days", the last day, is the sabbath.
The sequence was likely lost to the children of Israel while in Egyptian captivity and so God (again) revealed it in Exodus 16.
NOTE that in Exodus 16 God commands his followers to KEEP the sabbath...BEFORE the old covenant was discussed or agreed upon. This makes sense since he created the sabbath BEFORE any covenants were made. So the sabbath FALLS out side of any covenants as a holy thing of God in and of itself.
Regarding a seventh day . . . your citation seems to be irrelevant. There is no place in the pre-Mosaic covenants that a special day of religious observation is mentioned, or even hinted, AFIK. On the seventh day of the Creation episode, God rested. It doesn't even hint that Adam also rested, does it? Unless it was when he was anaesthetized for the removal of a rib. Hmm?