The concept of "Original Sin" was developed after the NT was written. It found acceptance in order to justify Infant Baptism. Many Church Fathers saw sin having been introduced by Cain, not by Adam.
John 3:16 does not say that "God gave his son so that people could kill him". It demands "belief". That belief is not speaking of "mental assent". Rather, the concept is of "allegiance" (works).
The Hebrews thought of "salvation" corporately, nationally.
Explanations for the reason and efficacy of Jesus' (sacrificial) death have gone through several major iterations. Augustine's idea lasted almost 1000 years until Anselm brought in his ideas, which were based on medieval concepts. Others followed with their "explanations", including Abelard, Pelagius, Thomas Aquinas, and so forth. Why does God only love people because they killed his son? Who received the ransom payment-- some said it was paid to Satan because he was holding humanity captive.
As you spend the billions of years singing praises, while Andromeda collides with the Milky Way and the Sun dies, think of me. Who wants to live forever?
https://jwstudies.com/Revolutions_Part_4__Christian_Salvations.pdf
Doug