So important was the sacrificial ritual in the Temple that one wonders how Judaism survived when the sanctuary was destroyed. The question greatly exercised the Talmudic rabbis. The fact is that Temple or no Temple, Judaism did survive.
But the rabbis were concerned with a different issue: “now that we have no Temple, how can we obtain atonement?”
The Midrash Tanchuma gave a typical answer: “While the Temple stood, atonement came through the sacrifices; without the Temple, we have the Torah.”
There are many such statements. How do we replace the sacrifices as a means of atonement? By having a humble spirit (Sanh. 43b). By doing kindly deeds (Avot D’Rabbi Natan 4:5). By modesty within one’s house (Tanchuma). By hospitality (Chag. 27a). By controlling one’s instincts (Sanh. 43b).
Some sages felt that we had an even better means of atonement than before: “Charitable deeds are better than all the sacrifices” (Sanh. 49b).
“Atonement” indicates “at-one-ment”. Sacrifices, korbanot, from the Hebrew root for coming near, were not the only way to be at one with God. The same result could come from living a good and righteous life.
This does not mean that the sacrifices would be unnecessary when the Temple was rebuilt, but they would have to be accompanied by the sacrifice of the selfishness that gets in the way of a life with God.