“God invented the death penalty, knowing the wickedness of the fallen human race.”
Yet that same God did not execute Cain when He killed Abel. God even protected Cain so that no one would kill him. Genesis 4:15
He destroyed Sodom and allowed His Only Son to be crucified by a civil authority.
God still instituted the death penalty, and that is undeniable. Furthermore, he also gave civil government the power execute justice to deal with evil-doers (Romans 13:3), and that is not limited to God's people, but also to gentiles.