Nope. God commanded burnt offerings to take place only in the location He designated. The last place He designated for this purpose was the Temple in Jerusalem. In the absence of the Temple, it would be a violation of the Law to offer sacrifices.
Secondly, as you mentioned this method is an imperfect means of atonement, but Christ is the perfect means. He who had no sin, became sin for us, so that we might become the righteousness of God. His blood has cleansed us from all sin. His sacrifice was perfect. So there is no longer any need to make additional sacrifices for our sin, because He was the perfect sacrifice for all time.
Well, yes, you have done a fine job describing the Christian belief. However, this is not what the Hebrew scriptures teach. Let me break it down point by point.
1. Human sacrifice is forbidden by the Law. Therefore the death of Jesus could not be an acceptable sacrifice to God.
2. Some 'minor' points about blood sacrifices. In order to fulfill the Law, they must be physically unblemished, and they must be performed in the Temple. Neither of these conditions was met by Jesus's death.
3. This is a biggie. No other person can atone for your sins. This could not be more explicit:
The person who sins, he alone shall die. A child shall not share
the burden of a parent’s guilt, nor shall a parent share the
burden of a child’s guilt; the righteousness of the righteous
shall be accounted to him alone, and the wickedness of the wicked
shall be accounted to him alone.
Moreover, if the wicked one repents of all the sins that he
committed and keeps all My laws and does what is just and right,
he shall not die. None of the transgressions he committed shall
be remembered against him; because of the righteousness he has
practiced, he shall live. Is it my desire that a wicked person
shall die?--says the Lord God. It is rather that he shall turn
back from his ways and live. (Ezekiel 18:20-23)
without shedding of blood there is no forgiveness.
The author of Hebrews is wrong. Let's look at the passage from which this is supposedly derived:
[10] "If any man of the house of Israel or of the strangers that sojourn among them eats any blood, I will set my face against that person who eats blood, and will cut him off from among his people.
[11] For the life of the flesh is in the blood; and I have given it for you upon the altar to make atonement for your souls; for it is the blood that makes atonement, by reason of the life.
[12] Therefore I have said to the people of Israel, No person among you shall eat blood, neither shall any stranger who sojourns among you eat blood. (Leviticus 17:10-12)
The focus of this passage is not atonement, but rather is about dietary laws, specifically the prohibition against eating blood. NOWHERE does it even suggest that blood sacrifice is the only means of atonement (read the passage again!). The reason it doesn't is that such a statement is simply untrue! There are many other types of sacrifice described in the Law for atonement for sin (offerings of grain or treasure, for example).
Furthermore, sacrifices were not simply for the purpose of atoning for sin. They were also offered for thanksgiving and for ritual purification.
For the most part, sacrifices only expiate unintentional sins, that is, sins committed because a person forgot that this thing was a sin. No atonement is needed for violations committed under duress or through lack of knowledge, and for the most part, sacrifices cannot atone for malicious, deliberate sin. In addition, sacrifices have no expiating effect unless the person making the offering sincerely repents his or her actions before making the offering, and makes restitution to any person who was harmed by the violation.
In the absence of the sacrificial system, forgiveness for sin comes from repenting and turning back to God and his Law. Asking for forgiveness from those we have wronged. If possible, making right our wrongs. God promises repeatedly in the Hebrew scriptures to forgive those who turn to him. There are passages in the Hebrew scriptures which explicitly state that sacrifice is NOT necessary for atonement:
The sacrifice acceptable to God is a broken spirit;
a broken and contrite heart, O God, thou wilt not despise. (Psalm 51:17)
To do righteousness and justice
is more acceptable to the LORD than sacrifice. (Proverbs 21:3)
For I desire steadfast love and not sacrifice,
the knowledge of God, rather than burnt offerings. (Hosiah 6:6)
Sacrifice and offering thou dost not desire;
but thou hast given me an open ear.
Burnt offering and sin offering
thou hast not required. (Psalm 40:6)
[6] "With what shall I come before the LORD,
and bow myself before God on high?
Shall I come before him with burnt offerings,
with calves a year old?
[7] Will the LORD be pleased with thousands of rams,
with ten thousands of rivers of oil?
Shall I give my first-born for my transgression,
the fruit of my body for the sin of my soul?"
[8] He has showed you, O man, what is good;
and what does the LORD require of you
but to do justice, and to love kindness,
and to walk humbly with your God? (Micah 6:6-8)
For it is impossible for the blood of bulls and goats to take away sins.
This directly contradicts the Torah.
And all its fat he shall burn on the altar, like the fat of the sacrifice of peace offerings; so the priest shall make atonement for him for his sin, and he shall be forgiven. (Leviticus 4:26)
Since you are a jew and you don't beleive that Jesus is the Messiah, then this probably means little to you, so I ask you, how can you atone for sin without the shedding of blood, without a sacrifice to God?
Repent. Ask forgiveness of those we have wronged (God and/or others). Seek to make it right. Pretty much exactly what Christians must do when they sin.