By the resurrection of Jesus Christ from the dead !
1 Pet 1:2-3
2 Elect according to the foreknowledge of God the Father, through sanctification of the Spirit, unto obedience and sprinkling of the blood of Jesus Christ: Grace unto you, and peace, be multiplied.
3 Blessed be the God and Father of our Lord Jesus Christ, which according to his abundant mercy hath begotten us again unto a lively hope by the resurrection of Jesus Christ from the dead,
Here we have by Divine inspiration that the resurrection of Christ, by way of His Redeeming Death, is being viewed as the meritorious cause of the New Birth performed by the Spirit of the Covenant, so it is feasible to call the Second Man Adam, who is Christ an Quickening Spirit 1 Cor 15:45
45 And so it is written, The first man Adam was made a living soul; the last Adam was made a quickening spirit.
That word quickening is the greek word zōopoieō and means:
to produce alive, begat or bear living young
2) to cause to live, make alive, give life
a) by spiritual power to arouse and invigorate
b) to restore to life
to give increase of life: thus of physical life
d) of the spirit, quickening as respects the spirit, endued with new and greater powers of life
3) metaph., of seeds quickened into life, i.e. germinating, springing up, growing
As the Risen Adam, having paid for the sins of all for whom He died, for all whom sins had been laid to His Charge Rom 4:25, and now having satisfied God's Law and Justice in their behalf, they have the right to live Spiritually before God, so He causes them to Live, He gives them Spiritual Life.
He does this for His Seed Isa 53:10
10 Yet it pleased the Lord to bruise him; he hath put him to grief: when thou shalt make his soul an offering for sin, he shall see his seed, he shall prolong his days, and the pleasure of the Lord shall prosper in his hand.
This is why as the Risen Lord He is a Life Giving Spirit, to give Spiritual Life to all for whom He died. Thats why He said of His Sheep Jn 10:10
The thief cometh not, but for to steal, and to kill, and to destroy: I am come that they might have life, and that they might have it more abundantly.
Life here is Spiritual Life, which His Death for them shall merit ! And so by His Resurrection He lives and shall save them by His Life Rom 5:10
10 For if, when we were enemies, we were reconciled to God by the death of his Son, much more, being reconciled, we shall be saved by his life.
Thats what Paul means, shall be saved by His Life that of 1 Cor 15:45
45 And so it is written, The first man Adam was made a living soul; the last Adam was made a quickening spirit.
Christ must make Alive Spiritually, all for whom He died and rose again ! And He does by His Resurrection 1 Pet 1:3156
3 Blessed be the God and Father of our Lord Jesus Christ, which according to his abundant mercy hath begotten us again unto a lively hope by the resurrection of Jesus Christ from the dead,
This being begotten again means:
to produce again, be born again, born anew
2) metaph. to have one's mind changed so that he lives a new life and one conformed to the will of God