Christ dying instead of my old life doesn't answer the just demands of God's law because Christ wasn't the sinner. I am the sinner and therefore my "old life" from Adam must die.
Did our "old life" (other versions say "old man"; "old self") die "in Christ" when Christ, as the Son of Man, was crucified?
Yes:
Romans 6:6 "...
our old self was crucified with Him, in order that our
body of sin might be done away with, so that we would no longer be slaves to sin. 7 For he who has died is free from sin.
Q1: When did our "old life" die?
A1: When Christ, as the Son of Man, was crucified and died. That was almost 2000 years ago.
Q2: What is our "old life" according to the context?
A2: The "body of sin" (compare to Rom 7:18-20, i.e, our humanity indwelt by iniquity)
So "in Christ" my "old life" from Adam died in the humanity of Christ as the Son of Man. That's why Paul states that "when One died, all died". See 2 Cor 5:14
Christ's death, as the Son of Man, was literally our death.