Actually, you take out a part of the quote in Hebrews and need to read the whole of the three chapters 8, 9 and 10 and you will see that the New Covenant is in force now and we are, in fact, in the NC.
Hebrews 8:6. Christ is the mediator of the NC, not "will be".
Heb 9:16 For where a testament is, there must also of necessity be the death of the testator.
Heb 9:17 For a testament is of force after men are dead: otherwise it is of no strength at all while the testator liveth.
Christ is the testator of the NC and he has died, therefore the NC is in force now.
You will see this continue as you follow on through chapter 10.
All those promises made to Israel are available to us now because Christ has died, and not only that, he is risen to empower the new covenant he brought into being through his death on the cross.
Our sins are not yet to be forgiven, they are forgiven now: so says all the apostolic teaching and, indeed, by this God is able to write his law on our hearts to obey him. After all, that is what the life of discipleship is all about: obeying God through taking on his nature by Christ.
There is, of course, the unfolding of this because God had many, yet unborn, that he has chosen to save by faith [chapter 11] and so, like Abraham who had the covenant without the fulfilled promise, we press on toward the mark of the high calling of God. Now we are sealed into the covenant because we are in covenant but, when the last responds and Christ returns in clouds of glory, it will be revealed that we are the people of his covenant.
It is clear from the OT Scriptures you quote that Israel of the day did not have the NC because it had not yet been established but now it is established for Christ has died and brought it into force.
If you are not aware. Here is all the places the Greek word translated covenant can be found in Hebrews. Sometimes it is translated testament. There is plenty of context surrounding those passages which show that the Covenant is or can be in full affect for those of us who call on His name.
Heb 7:22 By so much was Jesus made a surety of a better
testament.
Heb 8:6 But now hath he obtained a more excellent ministry, by how much also he is the mediator of a better
covenant, which was established upon better promises.
Heb 8:8 For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new
covenant with the house of Israel and with the house of Judah:
Heb 8:9 Not according to the
covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt; because they continued not in my
covenant, and I regarded them not, saith the Lord.
Heb 8:10 For this is the
covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people:
Heb 9:4 Which had the golden censer, and the ark of the covenant overlaid round about with gold, wherein was the golden pot that had manna, and Aaron's rod that budded, and the tables of the
covenant;
Heb 9:15 And for this cause he is the mediator of the new
testament, that by means of death, for the redemption of the transgressions that were under the first
testament, they which are called might receive the promise of eternal inheritance.
Heb 9:16 For where a
testament is, there must also of necessity be the death of the testator.
Heb 9:17 For a
testament is of force after men are dead: otherwise it is of no strength at all while the testator liveth.
Heb 9:20 Saying, This is the blood of the
testament which God hath enjoined unto you.
Heb 10:16 This is the
covenant that I will make with them after those days, saith the Lord, I will put my laws into their hearts, and in their minds will I write them;
Heb 10:29 Of how much sorer punishment, suppose ye, shall he be thought worthy, who hath trodden under foot the Son of God, and hath counted the blood of the
covenant, wherewith he was sanctified, an unholy thing, and hath done despite unto the Spirit of grace?
Heb 12:24 And to Jesus the mediator of the new
covenant, and to the blood of sprinkling, that speaketh better things than that of Abel.
Heb 13:20 Now the God of peace, that brought again from the dead our Lord Jesus, that great shepherd of the sheep, through the blood of the everlasting
covenant,