No Temple, No Atonement? by slaveofone
Gentile nations benefited from having Israel offer sacrifices and supplication for them in ancient days. It was not uncommon for the priests to intercede daily with the Lord of Hosts even on the behalf of foreign nationals who claimed dominion over them.
Said R. Johanan: Woe be to the nations, they have lost, and they do not know even what they have lost! When the Temple was in existence, the altar atoned for their sins, but now who shall atone for their sins?
Babylonian Gemara, Sukkah 4
The author of Hebrews has an answer:
The former priests, on the one hand, existed in greater numbers because they were prevented by death from continuing, but Jesus, on the other hand, because He continues forever [resurrected from the dead], holds His priesthood permanently. Therefore He is able also to save forever those who draw near to God through Him, since He always lives to make intercession for them. For it was fitting for us to have such a high priest, holy, innocent, undefiled, separated from sinners and exalted above the heavens; who does not need daily, like those high priests, to offer up sacrifices, first for His own sins and then for the sins of the people, because this He did once for all when He offered up Himself. For the Law appoints men as high priests who are weak, but the word of the oath, which came after the Law, appoints a Son, made perfect forever.
Hebrews 7:23-28
The oath that the author of Hebrews speaks of which came after the Law is thus:
YHWH has sworn and will not change his mind, you are a priest forever according to the order of Melchizadek.
Psalm 110:4
The author of Hebrews interprets this to mean that YHWH prepared for a new and better priesthood in place of the Levites and a new and better High Priest in place of Aaron.
For when the priesthood is changed, of necessity there takes place a change of law also.
Hebrews 7:12
Of course, this Hebraic perspective also gels nicely with the concept of a change of covenant (from temporal to eternal). So the nations have lost nothing by the loss of the temple. In fact, they have gained atonement despite it.