The Old Covenant was made with a nation through a mediator--Moses (
Exodux 19:3--24:8). God did not deal with the people of Israel directly.
And as Moses was the mediator of the Old Covenant (
Exodus 19:3--24:8) between God and the nation Israel, so Jesus is the Mediator of the New Covenant between God and the body of Christ (
Hebrews 8:6), each one individually.
At the time the new covenant promise was made in Jer 31, the people of God were the "house of Israel and the house of Judah." But the covenant would be made through a
single mediator, who was not named in Jer 31, but
is named in
Hebrews 8:6.
The New Covenant is made with the body of Christ, one
individual at a time, through Jesus, its single Mediator.
There is no "beginning of the New Covenant" for any nation, or any person.
You
enter the New Covenant which has been in existence since the resurrection of Jesus Christ.
The New Covenant is
mediated through Jesus Christ and that is where you go to enter it with God.