The first thing that is crucial to understanding Hebrews is that we serve the only true God. He is not like the gods of the heathens. There are a few verses that I believe are essential to understanding who this God is:
"Thus saith YHVH of hosts, the God of Israel; Put your burnt offerings unto your sacrifices, and eat flesh.
For I spake not unto your fathers, nor commanded them in the day that I brought them out of the land of Egypt, concerning burnt offerings or sacrifices:
But this thing commanded I them, saying, Obey my voice, and I will be your God, and ye shall be my people: and walk ye in all the ways that I have commanded you, that it may be well unto you.
But they hearkened not, nor inclined their ear, but walked in the counsels and in the imagination of their evil heart, and went backward, and not forward." (Jeremiah 7:21-24)
God did not give the Israelites any ordinances concerning sacrifices when he brought them out of Egypt (except for Deuteronomy 17:1 in which He tells them specifically what they are not to sacrifice to Him). Notice the beginning of Leviticus says:
"And YHVH called unto Moses, and spake unto him out of the tabernacle of the congregation, saying,
Speak unto the children of Israel, and say unto them, If any man of you bring an offering unto YHVH, ye shall bring your offering of the cattle, even of the herd, and of the flock." (Leviticus 1:1-2)
We are not told when God spoke to Moses here, so unless we contradict Jeremiah, Leviticus must have been written after Deuteronomy. The first word God says concerning sacrifices is "IF", which means absolutly none of this is necessary. Our Father is saying "If one wishes to offer sacrifices, these are the necessary rules to follow, but none of them are necessary for anything." God has no desire for sacrifices:
"And Samuel said, Hath YHVH [as great] delight in burnt offerings and sacrifices, as in obeying the voice of YHVH? Behold, to obey is better than sacrifice, and to hearken than the fat of rams." (1 Samuel 15:22)
"To what purpose is the multitude of your sacrifices unto me? saith YHVH: I am full of the burnt offerings of rams, and the fat of fed beasts; and I delight not in the blood of bullocks, or of lambs, or of he goats.
When ye come to appear before me, who hath required this at your hand, to tread my courts?
Bring no more vain oblations; incense is an abomination unto me; the new moons and sabbaths, the calling of assemblies, I cannot away with; it is iniquity, even the solemn meeting." (Isaiah 1:11-13)
"For thou desirest not sacrifice; else would I give it: thou delightest not in burnt offering.
The sacrifices of God are a broken spirit: a broken and a contrite heart, O God, thou wilt not despise." (Psalm 51:16-17)
"Sacrifice and offering thou didst not desire; mine ears hast thou opened: burnt offering and sin offering hast thou not required." (Psalm 40:6)
The only reason God gave the rules for sacrifice is because men desired to offer sacrifices. They followed after the idols of their fathers, so God gave them the sacrificial system to blind them. Check this out:
"I lifted up mine hand unto them also in the wilderness, that I would scatter them among the heathen, and disperse them through the countries;
Because they had not executed my judgments, but had despised my statutes, and had polluted my sabbaths, and their eyes were after their fathers' idols.
Wherefore I gave them also statutes that were not good, and judgments whereby they should not live;
And I polluted them in their own gifts, in that they caused to pass through [the fire] all that openeth the womb, that I might make them desolate, to the end that they might know that I am YHVH." (Ezekiel 20:23-26)
If there should be a sacrifice that was extra abominable towards God, it was this:
"When thou art come into the land which YHVH thy God giveth thee, thou shalt not learn to do after the abominations of those nations.
There shall not be found among you any one that maketh his son or his daughter to pass through the fire, or that useth divination, or an observer of times, or an enchanter, or a witch,
Or a charmer, or a consulter with familiar spirits, or a wizard, or a necromancer.
For all that do these things are an abomination unto YHVH: and because of these abominations YHVH thy God doth drive them out from before thee." (Deuteronomy 18:9-12)
The first abomination that God says we shall not do is sacrifice our children. This is not what our God requires:
"They have built also the high places of Baal, to burn their sons with fire for burnt offerings unto Baal, which I commanded not, nor spake it, neither came it into my mind" (Jeremiah 19:5)
Even if one believes in the trinitarian thing, they still must say Yeshua is God's son, and that he is 100% human. So if his death was a sacrifice, it was an abomination. Yeshua himself says:
"But go ye and learn what that meaneth, I will have mercy, and not sacrifice: for I am not come to call the righteous, but sinners to repentance." (Matthew 9:13)
Why would a human sacrifice offer the ultimate "propitiation" or "atonement" for our sins? There are many things inconsistent with this idea, but there are also several English bibles that use this term. Propitiation means to appease an angry god. If God doesn't want sacrifice, then what would be appeasing to Him about a human sacrifice? Surely this word, in 1 John 2:2, 1 John 4:10, and Hebrews 2:17 has been mistranslated. In Luke 18:13, it is translated as "merciful", which makes a lot more sense.
The book of Hebrews becomes a lot clearer when we understand that the author is speaking figuratively (I know everyone hates that word), and when we understand what Yeshua means when he says:
"Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil." (Matthew 5:17)
Yeshua was not the "one sacrifice to end all sacrifice". He came to teach us the word of God, and his life abolished the sacrificial system because it was never the Law to begin with. He offered the ultimate sacrifice- to deny his own life.
In Hebrews, Yeshua is called "high priest", "a sacrifice", and the "veil" to the Holy of Holiest. Yeshua cannot literally be a priest in heaven, passing through a cloth version of himself, to offer himself as a sacrifice. This must be taken figuratively.
God has no desire for sacrifices, Yeshua was not a literal human sacrifice to appease an angry God, and the book of Hebrews uses figurative language to teach us a deeper truth. So my answer is no, Yeshua did not literally offer his blood on the mercy seat of a heavenly temple.