The English word chosen in Heb. 9:28 as "save" or "salvation" is the Greek word "σωτηρία" or "soteria" and it means "deliverance, salvation". It is used for "welfare, prosperity, deliverance, preservation, salvation, safety". (Strong's Gr. 4991)
The root word is "sozo", Strong's Gr. 4982 which means to rescue, save. Thayer's Greek Lexicon has the meaning for this usage in Heb. 9:28 under definition "c. future salvation". (1)
Most commentators try to make this fit within the concept of heavenly salvation. However, when we keep in mind the first audience perspective, the immediate circumstances of those who heard and read these words in AD 60-65 when the book of Hebrews was written, we might understand more clearly that the word the English translators used for "soterian" should have been deliverance or preservation.
The verse is confusing because many readers skip over "not to deal with sin". His first coming was to take away the sins of the world for those who will believe, and He became the sacrifice that is acceptable to God as the Lamb slain from the foundation of the world (Rev. 13:8). His sacrifice during His first manifestation was the true and final sin offering "to make an end of sins" (Dan. 9:24), to make an end of the animal sin offerings at that temple in Jerusalem.
When He died on the cross, salvation was assured for our souls, our spirits at that time. Anyone who had believed and been immersed (baptized) in Christ had the salvation promise of our eternal home in heaven.
So, His second appearance (presence) was not to deal with salvation from sins, because they already had that. His second appearance in that same generation was for judgment against those who pierced Him (Rev. 1:7) and to rescue His saints from the tribulations, persecutions and tyranny of the Sanhedrin and Roman army.
This verse is best rendered in the CJB.
"so also the Messiah, having been offered once to bear the sins of many, will appear a second time, not to deal with sin, but to deliver those who are eagerly waiting for him." (Heb. 9:28, CJB)
He was saving them, rescuing them, preserving the remnant, and delivering them out of the tribulations while they yet lived here on earth, to preserve their earthly lives.
The warning voice "let us leave this place" reportedly heard by the Christians still in Jerusalem during the lull of the battle when Cestius unexpectedly retreated (circa Nov AD 66) is said to be when they fled to Pella.
"It then happened that Cestius was not conscious either how the besieged despaired of success, nor how courageous the people were for him; and so he recalled his soldiers from the place, and by despairing of any expectation of taking it, without having received any disgrace, he retired from the city, without any reason in the world." (2)
"The members of the Jerusalem church by means of an oracle, given by revelation to acceptable persons there, were ordered to leave the city before the war began and settle in a town in Peraea called Pella." (3)
"Besides these, a few days after that feast, on the one and twentieth day of the month Artemisius, [Jyar,] a certain prodigious and incredible phenomenon appeared: I suppose the account of it would seem to be a fable, were it not related by those that saw it, and were not the events that followed it of so considerable a nature as to deserve such signals; for, before sun-setting, chariots and troops of soldiers in their armor were seen running about among the clouds, and surrounding of cities. Moreover, at that feast which we call Pentecost, as the priests were going by night into the inner [court of the temple,] as their custom was, to perform their sacred ministrations, they said that, in the first place, they felt a quaking, and heard a great noise, and after that they heard a sound as of a great multitude, saying, "Let us remove hence." (4)
The sights and omens surrounding that Jewish-Roman war which Josephus as well as Tacitus recorded were astounding. And, yet our Lord had warned His disciples of all of these in Matt. 24, Mark 13, and Luke 21.
"20 And when ye shall see Jerusalem compassed with armies, then know that the desolation thereof is nigh.
21 Then let them which are in Judaea flee to the mountains; and let them which are in the midst of it depart out; and let not them that are in the countries enter thereinto.
22 For these be the days of vengeance, that all things which are written may be fulfilled.
23 But woe unto them that are with child, and to them that give suck, in those days! for there shall be great distress in the land, and wrath upon this people.
24 And they shall fall by the edge of the sword, and shall be led away captive into all nations: and Jerusalem shall be trodden down of the Gentiles, until the times of the Gentiles be fulfilled.
25 And there shall be signs in the sun, and in the moon, and in the stars; and upon the earth distress of nations, with perplexity; the sea and the waves roaring;
26 Men's hearts failing them for fear, and for looking after those things which are coming on the earth: for the powers of heaven shall be shaken.
27 And then shall they see the Son of man coming in a cloud with power and great glory.
28 And when these things begin to come to pass, then look up, and lift up your heads; for your redemption draweth nigh." (Luke 21:20-28, KJV)
The English word “redemption” in Luke 21:28 is Strong’s Gr 629 – “ἀπολύτρωσις” or “apolutrósis”. It means “a release effected by payment of ransom, redemption, deliverance. Thayer’s Gr. Lexicon Definition 2 – “deliverance from the hatred and persecutions of enemies by the return of Christ from heaven.”
They had already been bought back / redeemed from their sins if they believed and were baptized (Mark 16:16), but they were also released / delivered from their situation, from harm, from the persecution and the dangers of the war by His return to destroy Jerusalem and that temple.
The people saw these visions in the sky. I am absolutely certain that Caiaphas also saw His return, just as Jesus had told him (Matt. 26:64).
Christ returned to rescue them, and deliver them from harm so that they could go forth from Jerusalem, and live to teach the gospel throughout all the ages of the Messiah and His "ecclesia" - "to the ages of the ages" (Eph.3:21 YLT). And, thus the voice of the Lord roared from Zion, and from Jerusalem (Joel 3:16; Amos 1:2; Micah 4:2).
1) Strong's Gr. 4991 - Biblehub
2) Josephus Flavius AD 75, Wars II, XIX, 7 - here
3) Eusebius c. AD 325, Book III, c.5 - here
4) Josephus Flavius AD 75, Wars VI, V, 3 - here