While Paul touches on the salvation of the Jews under the Law of Moses, Hebrews deals more thoroughly with the question, although the point of Hebrews is to demonstrate the superiority of the covenant under Christ to the Mosaic covenant.
To see the point, we need to trace a couple of thoughts through the text, beginning with the author’s doctrine of “once for all” salvation.
We should start, though, back in Romans —
(Rom 6:9-10 ESV) 9 We know that Christ, being raised from the dead, will never die again; death no longer has dominion over him. 10 For the death he died he died to sin, once for all, but the life he lives he lives to God.
The Greek for “once for all” is ἐφάπαξ (ephapax), meaning all at once and never again (BDAG).
Paul’s point, of course, is that Jesus was crucified just once, and this sacrifice is sufficient for all time and for all who will follow him. His one sacrifice is fully sufficient for all and never needs to be repeated.
It’s quite unprovable, but I think the Hebrews writer built much of his book on this verse (or the same argument made by Paul in person or by other means). The same word keeps showing up in Hebrews for the same point.
(Heb 7:26-27 ESV) For it was indeed fitting that we should have such a high priest, holy, innocent, unstained, separated from sinners, and exalted above the heavens. 27 He has no need, like those high priests, to offer sacrifices daily, first for his own sins and then for those of the people, since he did this once for all when he offered up himself.
Unlike the Mosaic priests, Jesus — as a priest after the order of Melchizedek (that is, a priest of God who is not a Levite) — offered but one sacrifice, a sacrifice sufficient to be “once for all,” that is, to forgive all sins of all people forever. The cross is enough to forgive everyone, although not everyone chooses to accept the grace offered.
(Heb 7:28 ESV) 28 For the law appoints men in their weakness as high priests, but the word of the oath, which came later than the law, appoints a Son who has been made perfect forever.
The author then explains that God’s oath appoints Jesus as high priest “made perfect forever.” Two oaths are in mind. First, there is the Abrahamic oath that God would bless Abraham and his descendants (Heb 6:13-16, referring to Gen 22:17). Added to this is the oath of Psalm 110 (referenced in Heb 7:20-22):
(Psa 110:1 ESV) 4 The LORD has sworn and will not change his mind, “You are a priest forever after the order of Melchizedek.”
And so Jesus is made such a priest “forever.” And so Jesus, by offering his once-for-all sacrifice, becomes a priest forever — indeed, he is made “perfect forever.”
Notice the interplay: To be perfect forever, one must have the benefit of a once-for-all sacrifice.
A couple of chapters later, the author pictures the new, true Jerusalem and the Temple in heaven (a concept we’ve discussed before), awaiting the Second Coming to be joined with the earth, as prophesied in Rev 21-22.
(Heb 9:11-12 ESV) But when Christ appeared as a high priest of the good things that have come, then through the greater and more perfect tent [or tabernacle] (not made with hands, that is, not of this creation [but in heaven]) 12 he entered once for all into the holy places, not by means of the blood of goats and calves but by means of his own blood, thus securing an eternal redemption.
So when Jesus ascended to heaven after his resurrection, he entered the “more perfect tabernacle,” that is, the Temple in heaven, and offered his blood as the once-for-all sacrifice needed for “eternal redemption.”
(Heb 10:1 ESV) For since the law has but a shadow of the good things to come instead of the true form of these realities, it can never, by the same sacrifices that are continually offered every year, make perfect those who draw near.
The Law could not “make perfect” the Jewish worshipers because the sacrifices had to be repeated over and over, year after year, and day after day. Only a once-for-all sacrifice could make them perfect forever.
(Heb 9:25-26 ESV) 25 Nor was it to offer himself repeatedly, as the high priest enters the holy places every year with blood not his own, 26 for then he would have had to suffer repeatedly since the foundation of the world. But as it is, he has appeared once for all at the end of the ages to put away sin by the sacrifice of himself.
The Greek for “put away” refers to annulling something. To make sin entirely defeated, we need a once-for-all sacrifice to make us “perfect forever.”
(Heb 10:12-14 ESV) 12 But when Christ had offered for all time a single sacrifice for sins, he sat down at the right hand of God, 13 waiting from that time until his enemies should be made a footstool for his feet. 14 For by a single offering he has perfected for all time those who are being sanctified.
The result of Jesus’ once-for-all sacrifice is forgiveness “for all time” so that Jesus’ followers are “perfected for all time.” That is, just as Jesus’ sacrifice was once for all so that he would be perfect forever, we enter into Jesus at baptism (Heb 10:22), receive once-for-all salvation and are ourselves made perfect forever — as we are being sanctified, that is, made more and more holy in fact. Although we are not perfect in reality, God sees us as perfect forever, while we are growing in Jesus to become more and more like him.