To my way of seeing this...It is not good enough to say the original covenant. As I said, God made two covenants with Abraham. Those in my mind are the original covenants. The Sinai covenant is a distinct covenant which is not made with Abraham.
The Exodus from Egypt under Moses, was a fulfillment of the covenant made in Genesis 15. Passover and the feast of unleavened bread are memorials of Gods fulfillment of promises made to Abraham. The nation of Israel is back there today as a result of that covenant. It is a covenant God keeps unto the natural seed of Abraham.
I believe that is why Israel is called God's firstborn. Two portions in Abraham....
One: temporal and earthly (a shadow) Moses
One: eternal and heavenly...( a reality) Jesus
Those of the circumcision in the foreskin of the flesh, which are believers share in both portions = firstborn.
The 1st covenant....
Ge 15:18 In the same day the LORD made a covenant with Abram, saying, Unto thy seed have I given this land, from the river of Egypt unto the great river, the river Euphrates:
The 2nd covenant....
Those of the uncircumcision which believe have a share equally with the circumcision.
Ge 17:4 As for me, behold, my covenant is with thee, and thou shalt be a father of many nations.
So when you say original covenant, which do you refer.