There are undoubtedly symbols in this passage. Fortunately, we are told what several of the symbols represent.
through the veil, that is to say, his flesh; (Hebrews 10:20)
Jesus is the antecedent for “his” in this verse. The veil is a symbol for Christ; specifically, that it was His body that was sacrificed on our behalf.
Blood of sacrificial animals
The blood of animals sacrificed in the temple was a symbol for the blood of Christ to be shed as an atoning sacrifice for redemption (see passage in section “the holy place”).
The holy place
This refers to the presence of God.
For Christ is not entered into the holy places made with hands, which
are the figures of the true; but into heaven itself, now to appear in
the presence of God for us: (Hebrews 9:24)
This was understood by ancient Israel—the second veil led into the holiest location of all, the “Holy of Holies”, which was understood to be (or to represent) the presence of God.
From Hebrews 9:
And after the second veil, the tabernacle which is called the Holiest
of all; (verse 3)
But into the second went the high priest alone
once every year, not without blood, which he offered for himself, and
for the errors of the people: (verse 7)
But Christ being come an
high priest of good things to come, by a greater and more perfect
tabernacle, not made with hands, that is to say, not of this building;
Neither by the blood of goats and calves, but by his own
blood he entered in once into the holy place, having obtained eternal
redemption for us. (verse 12)
Why “enter boldly”?
Entering the presence of God should be terrifying if one is unprepared. Without a mediator (and without having accepted the mediator’s terms) the prospects don’t look good:
From Hebrews 10:
29 Of how much sorer punishment, suppose ye, shall he be thought
worthy, who hath trodden under foot the Son of God, and hath counted
the blood of the covenant, wherewith he was sanctified, an unholy
thing, and hath done despite unto the Spirit of grace?
30 For we know
him that hath said, Vengeance belongeth unto me, I will recompense,
saith the Lord. And again, The Lord shall judge his people.
31 It is a
fearful thing to fall into the hands of the living God.
I understand the message of the passage in the OP to be, then, that because of the atoning sacrifice of Jesus Christ, it is possible to be prepared to enter the presence of God with confidence.
The passage in Hebrews doesn’t explicitly reference when.
From Revelation 20:12 we learn that we will stand before God to be judged after the resurrection (see references to the resurrection in vs. 4-5):
And I saw the dead, small and great, stand before God; and the books
were opened: and another book was opened, which is the book of life:
and the dead were judged out of those things which were written in the
books, according to their works.
Will people enter the presence of God at other times? The passage in Hebrews does not preclude this, but it does not appear to directly answer that question either.
Under Levitical ritual, only the high priest could enter the holy place, and the blood of animals was required for entrance.
Hebrews teaches that we can become prepared to enter the holy place—the presence of God—and need not do so in terror—because of the atoning blood of Jesus Christ, which offers not only forgiveness and redemption, but sanctification as well.