Jesus is the Sabbath. Why did God bless the Sabbath day? Because, He rested. Did he really rest? or did he rest in what Jesus did at the cross. I don't want to detur you, but what do you think? By trusting in what Jesus did at the cross you are keeping the Sabbath.
But when we go back there is no such allusion found as it is written:
Gen 2:1 Thus the heavens and the earth were finished, and all the host of them.
Gen 2:2 And on the seventh day God ended his work which he had made; and he rested on the seventh day from all his work which he had made.
Gen 2:3 And God blessed the seventh day, and sanctified it: because that in it he had rested from all work which God created and made.
We note that the Seventh day was connected to the first 6 in that God blessed it and sanctified it. Sanctified it means to set it apart for holy use. And the reason is clear that it was because he rested from the work of creating the world.
There is here no allusion to the cross that can be taken from these verses. It might also be good to point out that when it was made thus it was done so before sin came to this world which comes in the next chapter.
This also infers that the Sabbath at this point had no connection to sin or its effect at all. but finds its meaning in the creation of the world itself.
However I do not right off what you have said here because there were other Sabbaths similar to the 7th day Sabbath that were added by God through Moses which did indeed find their meaning and connection directly to redemption.