Hebrews 8, 9, and 10 are irrefutable that the Jeremiah 31 new covenant is being mediated by Jesus and it took effect when he died.
Hebrews 8 states Jesus is mediating, not will mediate, the new covenant, and in verses 8-10 it shows that covenant is the Jeremiah 31 new covenant with the House of Israel:
Heb 8:6 But as it is, Christ has obtained a ministry that is as much more excellent than the old as the covenant he mediates is better, since it is enacted on better promises.
Heb 8:7 For if that first covenant had been faultless, there would have been no occasion to look for a second.
Heb 8:8 For he finds fault with them when he says: “Behold, the days are coming, declares the Lord, when I will establish a new covenant with the house of Israel and with the house of Judah,
(Quotes Jeremiah 31, and the prophesy that a new covenant was coming)
Heb 8:9 not like the covenant that I made with their fathers on the day when I took them by the hand to bring them out of the land of Egypt. For they did not continue in my covenant, and so I showed no concern for them, declares the Lord.
Heb 8:10 For this is the covenant that I will make with the house of Israel after those days, declares the Lord: I will put my laws into their minds, and write them on their hearts, and I will be their God, and they shall be my people.
Hebrews 9 states that the new covenant Jesus mediates is His last will and Testament, that took effect at His death, as all last will and Testaments do:
Heb 9:15 Therefore he is the mediator of a new covenant, so that those who are called may receive the promised eternal inheritance,
since a death has occurred that redeems them from the transgressions committed under the first covenant.
(Is the mediator, not will be, and who’s death has occurred? Jesus’ death)
Heb 9:16 For where a will is involved, the death of the one who made it must be established.
Heb 9:17 For a will takes effect only at death, since it is not in force as long as the one who made it is alive.
Heb 9:18 Therefore not even the first covenant was inaugurated without blood.
Notice that the called obtain the promised inheritance from the last will and Testament that took effect at His death, verse 9:15
God always has a law, and the new covenant is a legal document that gives the called an inheritance - as in inheriting eternal life.
Hebrews 10 confirms that the once for all time sacrificial offering of Himself established the Jeremiah 31 new covenant where God puts His laws in the hearts and minds of those being sanctified:
Heb 10:14 For by a single offering he has perfected for all time those who are being sanctified.
Heb 10:15 And the Holy Spirit also bears witness to us; for after saying,
Heb 10:16 “This is the covenant that I will make with them after those days, declares the Lord: I will put my laws on their hearts, and write them on their minds,”
Heb 10:17 then he adds, “I will remember their sins and their lawless deeds no more.”
Heb 10:18 Where there is forgiveness of these, there is no longer any offering for sin.
Currently per Romans 11 only a remnant of the elect nation of Israel believes in Jesus and is in their own new covenant God has made with the House of Israel and thus have Gods indwelling Holy Spirit within them, which is how Gods laws are written in their hearts, and the rest are blinded until the deliverer comes out of Zion.
Rom 11:7 What then? Israel failed to obtain what it was seeking. The elect obtained it, but the rest were hardened,
Rom 11:25 Lest you be wise in your own sight, I do not want you to be unaware of this mystery, brothers: a partial hardening has come upon Israel, until the fullness of the Gentiles has come in.
Rom 11:26 And in this way all Israel will be saved, as it is written, “The Deliverer will come from Zion, he will banish ungodliness from Jacob”;
Gentiles as wild Olive branches are grafted onto the Olive tree of Israel, amid the natural branches, and thus by faith gentiles enter into the new covenant with the House of Israel.
Rom 11:17 But if some of the branches were broken off, and you, although a wild olive shoot, were grafted in among the others and now share in the nourishing root of the olive tree,
Rom 11:18 do not be arrogant toward the branches. If you are, remember it is not you who support the root, but the root that supports you.