Hebrews 9:22

‘And according to the law, I may almost say, all things are cleansed with blood, and apart from shedding of blood there is no remission.'

Indeed the Law made it quite clear, that ‘apart from the shedding of blood' there is no cleansing, there ‘is no remission (of sin)'. It tells us that all in the world is seen as tainted by sin, and that this taint of sin can only be dealt with by death, by the shedding of blood. By this, sin is seen as having affected everything that is. It is seen as rampant and the world as therefore cut off from God. And to remedy that requires death, a special death. For the wages of sin is death.

The Law therefore reveals that removal of the taint of sin can only be dealt with by the shedding of blood. It is only by that means that anything, including the tabernacle, and to a lesser degree the camp of Israel, could become holy to Yahweh. It is indeed often asked, why so many sacrifices? And the answer is, because there were so many sins. But all awaited the one great sacrifice for sins, which was once-for-all and would never required to be repeated, for its sufficiency was more than enough for the whole world of all ages. In the end it was without the shedding of  that  Blood that there was no remission of sins.

‘I may almost say.' Other things were in fact also connected with cleansing such as fire and water for purifying captured wealth (Numbers 31:22). See also Numbers 16:46, where instant atonement is made for the rebellious people by the use of the fires from the altar borne in a censer, which however connects with the shedding of blood (compare Isaiah 6:5); Numbers 31:50 where atonement had to be made for not giving the Lord His portion of what was won as spoil in battle, by remedying the failure and doing exactly that; and Leviticus 5:11 where the very poor could offer fine flour as a sin offering. But these were very secondary and peripheral. It was the shedding of blood that was ever the most prominent.