Without the shedding of blood there can be no remission of sin.
Hebrews 9:22 And almost all things are by the law purged with blood; and without shedding of blood is no remission
Matthew 26:28 For this is my blood of the new testament (covenant), which is shed for many for the remission of sins.
The life is in the blood.
Genesis 9:4 But flesh with the life thereof, which is the blood thereof, shall ye not eat.
Leviticus 17:11 For the life of the flesh is in the blood: and I have given it to you upon the altar to make an atonement for your souls: for it is the blood that maketh an atonement for the soul.
By giving his life, Jesus Christ made atonement for the souls (lives) of the faithful of all ages.
Romans 5:11 And not only so, but we also joy in God through our Lord Jesus Christ, by whom we have now received the atonement.
The shedding of his blood = the giving of his life.
It was a supreme act of love.
John 15:13 Greater love hath no man than this, that a man lay down his life for his friends.
This was the extension of God’s love to mankind.
John 5:16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
Romans 5:8 But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us.
Christ gave his perfect, sinless, life to ransom the lives of the faithful.
Matthew 20:28 Even as the Son of man came not to be ministered unto, but to minister, and to give his life a ransom for many.
Christ is the promised redeemer
Ephesians 1:7 In whom we have redemption through his blood, the forgiveness of sins, according to the riches of his grace;
Colossians 1:14 In whom we have redemption through his blood, even the forgiveness of sins:
Jesus Christ succeeded where Adam failed. We are born in Adam, but we can be reborn in Christ by believing and obeying the gospel and being baptised by immersion in water.
Romans 5:19 For as by one man’s disobedience many were made sinners, so by the obedience of one shall many be made righteous.
1 Corinthians 15:22 For as in Adam all die, even so in Christ shall all be made alive.
Our faith in Christ's sacrificial death will be imputed for righteousness when he returns.
Romans 3:25 Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God;
I hope this helps.