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According to Reformed theology, when did the New Covenant start?

When instituting the Lord's Supper, Jesus Christ said (Luke 22:20, NIV):

In the same way, after the supper he took the cup, saying, “This cup is the new covenant in my blood, which is poured out for you.

And in Jeremiah 31 the new covenant is also mentioned, with the blessings of the covenant listed. Hebrews 8 talks about the new covenant superceding the old in some way (the details of which perhaps I will put in another question).

At which stage did this new covenant supersede the older covenant, according to Reformed theology?