As noted in the description of the Adventist Sanctuary Teaching, the doctrine asserts that the cleansing of the sanctuary in heaven started in 1844. 

In 1844, at the end of the prophetic period of 2300 days, He entered the second and last phase of His atoning ministry. It is a work of investigative judgment which is part of the ultimate disposition of all sin, typified by the cleansing of the ancient Hebrew sanctuary on the Day of Atonement. In that typical service the sanctuary was cleansed with the blood of animal sacrifices, but the heavenly things are purified with the perfect sacrifice of the blood of Jesus. (Adventist Fundamental Belief #24)

Therefore, if the Scriptures show a different time for the start of the portion of the Day of Atonement that dealt with the cleansing of the sanctuary from the corporate sins of the people, then we can be sure that the doctrine is not correct. This is exactly what we find when we examine the book of Hebrews. 

The Day of Atonement type, spelled out in Leviticus, pictures a corporate presentation of blood to make atonement for the sins of the people throughout the year. This one day was the only time that the high priest could enter into the Most Holy Place of the sanctuary to appear directly before God. At that time the priest would sprinkle the blood on the mercy seat, on the ark. The following highlights from Leviticus 16 spell out some of the details:

Lev 16:2  and the LORD said to Moses, "Tell Aaron your brother not to come at any time into the Holy Place inside the veil, before the mercy seat that is on the ark, so that he may not die. For I will appear in the cloud over the mercy seat.

This passage tells us that the Lord would appear in the cloud over the mercy seat, which is on the ark.  Aaron was not to come just whenever he wanted into that Most Holy Place.

Lev 16:15  "Then he shall kill the goat of the sin offering that is for the people and bring its blood inside the veil and do with its blood as he did with the blood of the bull, sprinkling it over the mercy seat and in front of the mercy seat.
Lev 16:16  Thus he shall make atonement for the Holy Place, because of the uncleannesses of the people of Israel and because of their transgressions, all their sins. And so he shall do for the tent of meeting, which dwells with them in the midst of their uncleannesses.

The high priest was to bring the blood of the sacrifice in and sprinkle it over the mercy seat. By doing so he was making atonement for the Holy Place, which was unclean from all the sins of the people. He would also cleanse the rest of the sanctuary.

It was the sins of the people that caused defilement. The Day of Atonement, therefore, was a picture of corporate cleansing of all the sins of those among the people of God. It involved cleansing the people, and the sanctuary which was defiled by God living in the midst of the people.

Lev 16:17  No one may be in the tent of meeting from the time he enters to make atonement in the Holy Place until he comes out and has made atonement for himself and for his house and for all the assembly of Israel.

Lev 16:33  He shall make atonement for the holy sanctuary, and he shall make atonement for the tent of meeting and for the altar, and he shall make atonement for the priests and for all the people of the assembly.

The first thing we will note is that this is not portraying an examination of each of the people. Rather, it is showing a corporate atonement by means of blood.  The activity in the sanctuary, performed by the high priest, was not a judgment, but an atonement.  Now there are aspects of judgment associated with the Day of Atonement, as those who did not participate were cut off. But the primary activity going on in the sanctuary was that of provision of blood for the sins of the people, and to cleans the defilement of sin.

Therefore, there is good reason to question the Sanctuary doctrine being a fulfillment of the Day of Atonement type, when the Adventist doctrine describes an investigation, rather than an atoning presentation of blood.

The book of Hebrews however removes any doubt as to when this cleansing provision of blood for all the people occurred in the heavenly fulfillment. And it was long before 1844.

The first clear reference to a corporate cleansing of sin in Hebrews occurs in Chapter 1.

Heb 1:1  Long ago, at many times and in many ways, God spoke to our fathers by the prophets,
Heb 1:2  but in these last days he has spoken to us by his Son, whom he appointed the heir of all things, through whom also he created the world.
Heb 1:3  He is the radiance of the glory of God and the exact imprint of his nature, and he upholds the universe by the word of his power. After making purification for sins, he sat down at the right hand of the Majesty on high,
Heb 1:4  having become as much superior to angels as the name he has inherited is more excellent than theirs.

The purpose of Hebrews is to show the superiority of Christ, and His covenant, and ministry to that of the Old Covenant. And right from the outset one of the things that shows Christ's superiority is His handling of sin.

Hebrews 1:3 tells us that Jesus made purification for sins, and having done that He sat down at the right hand of the Majesty on high.

This shows both kingly and priestly roles for Christ. He made purification for sins, a priestly act, and then reigns at God's right hand, the role of a king.

What is clear from the text is that before Jesus sits down He has already completed the priestly task of ministration for sins. He already made the corporate provision. He already made purification. This corporate purification certainly recalls the Day of Atonement service with its provision for the whole camp. This verse summarizes Christs activity in completing all of the blood work spelled out in the old testament type. It is all described in the past, fulfilled before the author wrote this book, in the first century.

Now this does not mean that Jesus' ministry as High Priest is over. Other articles will tough on this point. What it does mean is that the provision is already made for all sins, and the rites of sacrifice (on the cross) and presentation of blood (in the heavenly sanctuary) were already completed. Jesus already did all the priestly work necessary for purification by this time.

Two other passages in Hebrews 9 touch more fully on the Day of Atonement service.

Heb 9:11  But when Christ appeared as a high priest of the good things that have come, then through the greater and more perfect tent (not made with hands, that is, not of this creation)
Heb 9:12  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.

Jesus' entry here is described with a number of specifics.

1. Jesus entered as high priest into the sanctuary.

2. He entered by means of blood.  Blood was not necessary to enter the first compartment of the sanctuary. Blood was required, however, to enter the second compartment. So this entry of Jesus included ministration in the heavenly equivalent of the second compartment.

3. Jesus blood is said to be superior to that of goats and calves. While there are various sacrifices spelled out in the Old Testament, few involved entry into the sanctuary with blood. The reference to goats and calves reduces further the possibilities for the old testament service being referenced. Specifically, goats blood was only brought into the sanctuary on two occasions, both involving the Most Holy Place. The first service involving goat blood and entry into the sanctuary is the service to inaugurate the sanctuary (described in Leviticus chapters 7 and 8). The second is the Day of Atonement.

4. The entry of Jesus with blood secured eternal redemption. This shows the finality of the blood work Jesus is performing here.

With these points in mind, some have said that what is being described here is not the Day of Atonement cleansing, but the inauguration. In reality, however, it is both. Jesus is said in vs. 12 to enter "once for all." Just like His sacrifice for sins was once-for-all, and did not required various repetitions, at various times, so his entry was also once-for-all. Just as all the sacrifices in the Old Testament were fulfilled by Jesus' sacrifice, so all the entries with blood were fulfilled by this one entry and presentation as well.

Jesus died once, at one point in time. He does not need to die again. However, in the type it was not just death that was required. Blood had to be ministered by the priest. And we see here Jesus going before God and ministering His completed sacrifice in the presence of His Father. The once-for-all sacrifice is ministered once-for-all. The summary of it bringing in eternal redemption shows its finality. No more ministering of blood is needed. Jesus' one sacrifice has been completed, and presented.

The last passage that spells out the Day of Atonement fulfillment of the cleansing of the sanctuary is the most clear yet.

Heb 9:23  Thus it was necessary for the copies of the heavenly things to be purified with these rites, but the heavenly things themselves with better sacrifices than these.
Heb 9:24  For Christ has entered, not into holy places made with hands, which are copies of the true things, but into heaven itself, now to appear in the presence of God on our behalf.
Heb 9:25  Nor was it to offer himself repeatedly, as the high priest enters the holy places every year with blood not his own

In this passage we see the following:

1. It was necessary for the earthly sanctuary to be purified. It is necessary for the heavenly realities, of which the earthly were a copy, to be purified with better sacrifices.

2. The fulfillment of this cleansing is then spelled out. Christ has entered into heaven itself, to appear in the presence of God on our behalf.

3. This presentation of Christ before God, where He presents or offers Himself the completed sacrifice for sin, is contrasted with the entry of the high priest on the day of atonement.  The high priest had to enter in once every year, again and again, year after year.  However, Jesus entered once and presented Himself before God, and only had to do so once.

Just as the earthly high priest would minister blood in God's immediate presence while cleansing the earthly sanctuary, so Jesus ascended to God and ministered the sacrifice of Himself that had been made on the cross. This is described in the context of a passage discussing the cleansing of the heavenly things.

So we see from Hebrews that Jesus' death and ministration of His blood

- made purification for sin

- secured eternal redemption

- cleansed the heavenly things with better sacrifices

As this was all done before the time of the writing of Hebrews, it rules out the Adventist fulfillment which they see in 1844.