How can we gain atonement? If we want to have a good relationship with our Father in Heaven, what can we do to make things right once we have broken His heart by sinning? Hebrews 9:22 tells us that "without the shedding of blood, there is no atonement". But the fact is, you'll never find any similar statement or a statement supporting this in the Tanach anywhere. You will find that a passage in Leviticus 17:11 that tells us that blood atones for a life, but the context makes it clear that we are only allowed to use blood for atoning, and not for eating. Apparently, it's common in most cultures to eat blood, and G-d was telling us in this passage that we are forbidden to eat the blood of an animal. But as disgusting as eating blood is, it's not very important to this topic. Leviticus 4 tells us that if someone sins, then he can bring a bull (for a Kohen or the "entire assembly of Israel", Lev. 4:1-21), a male goat (for the ruler of Israel Lev. 4:22-26), or a female goat or female sheep (for a regular citizen of Israel, Lev. 4:27-35). Leviticus chapter 5 also mentions a guilt offering of a ram for sins against the sanctuary (for example, if a person walks into the Sanctuary in a state of ritual impurity), but that's really about it for offering blood sacrifices for sin. I should also mention that these are only if the sin was unintentional and the sin later became known to the person who sinned. If the person intentionally sins (for example, a person intends to eat pork and then does it), there is no sacrifice that can be brought to atone for this sin. The Torah plainly says in these two chapters that these sacrifices only apply if the sin was unintentional, presumably the person who sinned regrets the sin even though it wasn't intentional, because there is no other reason that a person would bring an offering for his sin unless he regrets it and wants to correct his relationship with G-d.
But we don't have the Sanctuary today, so these two offerings and all the laws associated with them can't apply today. So, now what do we do? Better yet, what does someone who sinned intentionally in the past and wants a good relationship with G-d do without these offerings to atone for him? After all, Numbers 15:30-31 tells us that the person who sins intentionally is cut off from Israel. Now, as we will see shortly, this person who intentionally sins is only cut off temporarily, and he's only cut off from Israel in the respect that he intentionally sinned and the rest of the community didn't. So what do we do today in the absence of the Sanctuary, and what does a person who intentionally sins do to repair the breach in his relationship with G-d? As it turns out, the answer is also in the Tanach, and it may surprise you to know that it isn't Jesus/Yeshua.
King David says in Psalm 40:7 (40:6 in Christian Bibles) tells us that G-d doesn't desire our offerings, but He has opened our ears. What does it mean to have our ears opened? There are many interpretations, but the most obvious one is that He has opened our ears to hear that we have messed up and that we have to take steps to atone for our sin before we can have a right relationship with our Father in Heaven again. What steps could we take? Isn't a blood sacrifice the only way to atone for sin? Isn't that what Hebrews 9:22 says? In 2 Samuel 12:13, King David was confronted with his sin by the prophet Nathan. Immediately, he acknowledged his sin and was cut to the heart and was remorseful. Nathan told him that his sin was already forgiven. He simply acknowledged that he sinned and felt bad about it, and he was forgiven, no need for sacrifices for his atonement. He wrote about this experience in Psalm 51:15-19. In verse 19 he gives us the secret to our atonement, he says "The offerings G-d desires are a broken spirit, a broken and humbled heart You will not despise, Oh G-d". Our repentance is one of the methods of atoning for our sin. If you need a good example of this in practise, read the book of Jonah, it's a great book, and it's a short book if you're concerned about time. According to various places in the New Testament, G-d couldn't have forgiven the people of Nineveh because they didn't bring a blood sacrifice. After repenting, we can go back to a life of devotion to G-d, which is better than sacrifice according to 1 Samuel 15:22. According to Hosea 14:2-3, Micah 6:6-8, 1 Kings 8:46-50, Jeremiah 7:3-11, Ezekiel 18:21-23, and Ezekiel 33:10-11, prayer and repentance are better than and have even more atonement power than sacrifices (since prayer and repentance can atone for people who intentionally sin). In fact, this is beyond the scope of this article, but Ezekiel 18 as a whole chapter actually tells us that nobody can die as an atoning death for anyone else, which rules out Jesus/Yeshua as a method for atonement. The reason is because human sacrifice is outright forbidden and it's very distasteful to G-d to kill the innocent to save the guilty.
So we know that sacrifices only atone for unintentional sins, and we know that repentance and prayer is better than sacrifice because it can atone for even intentional sins. Is there another way to gain atonement? According to Daniel 4:24 (4:27 in a Christian Bible), Hosea 6:6, Proverbs 21:3, Proverbs 16:6, Proverbs 11:4, and Proverbs 10:2, charity also atones. In fact, Proverbs 21:3 tells us that charity and justice is better than a sacrifice. So, just to clarify, G-d tells us in the Tanach that repentance and prayer, and charity are better than a sin sacrifice. So basically, Jesus/Yeshua doesn't look like a very good atonement plan anymore.
One last thought: You've heard and probably read passages in the New Testament like Romans 6:10, Hebrews 7:27, Hebrews 9:12, Hebrews 10:18 and Hebrews 10:18 that say that Jesus/Yeshua was a better high priest because his death atoned for sin once and for all. These passages make it clear that his death was enough to atone for all sin from that point on, so in the theology of the authors of these letters, there will be no more offerings brought to the Temple in Jerusalem. And it's easy to take these passages at their word since there is no Temple in Jerusalem, and since the working theology of Hebrews is that there is no atonement without blood sacrifice (Hebrews 9:22), the death of Jesus/Yeshua has to be the final sacrifice needed to atone for sin in the absence of the Temple. That's a problem, but it's only a problem because the authors of these two letters and any other statement that there will be no more sin sacrifices after Jesus/Yeshua didn't know that the Tanach already told us that this isn't true. They clearly didn't read their Tanach very well. Ezekiel chapters 40-47 detail a floor plan for the Third Temple, and they even include the information that uproots Paul's teachings and the teaching in the book of Hebrews. Ezekiel 42:22-25 tells us that the sin offerings will again be offered in the Temple in Jerusalem. Also up for consideration is the fact that Isaiah 56:7, Jeremiah 33:17-18, and Zechariah 14:21 all speak of the sacrificial Temple services being re-instituted in the future Messianic Age. These passages are almost universally accepted by Christian scholars as being Messianic and speaking of the End Days. So this leaves us with a few questions to ask you. Why do Romans and Hebrews contradict the Tanach if they are meant to be a continuation of the Word of G-d? If Jesus/Yeshua is the final sacrifice for sin as Hebrews 10:18 claims, why do the prophets in the Tanach say that the Temple services, including the sin offerings, will resume in the Third Temple in Jerusalem? And more importantly, why are there no passages in the Tanach that even hint that Jesus/Yeshua, or even the real Messiah, would be an offering for sin, especially the final sin offering? What's even more perplexing to me personally is the fact that Ezekiel 46:16-18 mentions that the Messiah can give gifts to his children as a part of their inheritance, so why has the Church literally fought wars to suppress the idea that Jesus/Yeshua had children? The most important question here is, if the Tanach already said that sacrifice isn't the only way to atone for sin (and it's actually the lowest level of atonement), and if repentance, prayer, and charity atone for sin even better than sacrifice, and that sin offerings will resume in the Third Temple, why would anyone accept what the New Testament says when it tells us that Jesus/Yeshua is the final sin sacrifice and is the only true atonement for our sins?