That’s a nice comment. Thank you.
The question is a big one and I’m not sure I can do a very good job of answering it briefly. But perhaps it helps to think of two main themes.
First, there is the temple-based sacrificial system, which is intended to deal with the routine, day-to-day sinfulness of God’s people, with the day of atonement ritual being climactic.
Secondly, there is the covenantal or Deuteronomic narrative theme (eg. Deut. 28:15-68), which tells a story about persistent, cumulative sin, rebellion against YHWH, refusal to walk in his ways, leading to national catastrophe, typically in the form of war, invasion, destruction, and exile. Because is faithful to his covenant(s) with his people, the hope invariably arises that once they have been punished, he will forgive and restore. So for example, Isaiah 40 speaks comfort to ruined Jerusalem that her warfare is ended and her iniquity is pardoned, and Isaiah goes on to describe the restoration of his people.
In this second scenario the usefulness of the temple as embodying the sacrificial system is called into question, and if it is destroyed, then clearly there is no provision for atonement. Under these circumstances, the suffering of Israel, perhaps focused in an individual, becomes sacrificial and redemptive. The servant song of Isaiah 53 is a good example—originally, I suspect, applied to the exile community or perhaps the descendants of the original exiles: eg. “his soul makes an offering for guilt” (Is. 53:10).
We find a similar convergence in the Maccabean literature: “And through the blood of those pious people and the propitiatory (hilastēriou) of their death, divine Providence preserved Israel, though before it had been afflicted” (4 Macc. 17:22).
The relevance of this for the New Testament is fairly obvious.