1. The universal experience of inner screwed-upness.
Something is wrong with me, and something is wrong with us. It has always been this way and it remains so.
The deep, inner individual and cultural experience of "seeds of destruction" (Thomas Merton) and "violence within" (Paul Tournier) is available to all sensitive seeker of answers to the corrupt human condition.
2. Something needs to be done about this.
Some kind of price needs to be paid to a God or gods or whatever is out there or in here. There ought to be something like "an eye for an eye and a tooth for a tooth." Justice must be served.
You'll find this basic ontological insight in all cultures in all times and all places. This has not changed as of today. All the "law and order" movies and TV dramas are rooted in the deep human sense that something must be done, justice must be served, things must be made right so as to return to order.
3. Life must be given where life has been taken.
No amount of money can make up for the damage we do when we hurt and "take life" from others. The only thing that comes close to making things right is by taking life from the violator. "Life" is more precious than inanimate material things. This is why cross-cultural sacrificial systems require the giving of life where life has been lost or reduced. "Life" can include plants (e.g., grain offerings), animals (from birds to bulls) and humans.
In our world throughout history most persons in most places have deep-believed in 1, 2, and 3. These three deep, human realities delineate a common language and a shared world-experience. Hence, sacrifice. Hence, a price must be paid. This is something all peoples, everywhere, have understood and still understand.
This is the broader context into which the cross of Christ is planted and understood. This is the universal condition into which, according the biblical narrative, God came. God, in agreement with 1, accommodated himself to 2 and substituted himself in 3. The Jesus-response to 1, 2, and 3 is:
A. All have sinned and fallen short of the glory of God.
B. God has paid the price, in Christ.
C. A once-for-all sacrifice of life has been given, in which humanity is given cleansing and freedom from our inner fallenness.
BTW - every worldview has its own atonement theory. I see the Jesus Way as the most creative and brilliant, in theory and experience.