Grenville,
There is no intermediary between God and His creation. God is the most merciful and He hears the supplicant whenever he calls on Him. God is always there to listen to sincere repentance and never turns away from the sincere. There is no need to accept any blood sacrifice. We are told that no matter how many good deeds you have done it will still prove insufficient to acquire for oneself paradise. We can only hope in the mercy of God alone.
That being said:
You will also notice that there are three types of atonement given for sin in the OT. The only atonement was not limited to blood sacrifice; i.e. charity, repentance, and blood sacrifice.
Leviticus 17:11:
"This is because the life of the flesh is in the blood, and I have given it to you upon the altar to make atonement for your souls; for it is the blood that makes atonement for the soul."
Is the above said verse justification for what you have stated about the need for blood atonement?
***Keep in mind also that the blood sacrifice was only required for unintentional sins.
Numbers 15:27-31
If a person sins unintentionally, then he shall offer a one-year-old female goat for a sin offering. The priest shall make atonement before the LORD for the person who goes astray when he sins unintentionally, making atonement for him that he may be forgiven . . . . The person who does anything defiantly, whether he is native or an alien, that one is blaspheming the LORD; and that person shall be cut off from among his people, because he has despised the word of the LORD and has broken His commandment, that person shall be completely cut off; his guilt shall be on him.
Jesus could not die for anyone's sins, whether committed intentionally or not. To begin with, the Jews were strictly prohibited from offering human sacrifices. The Bible warns the Jews that it is a grave sin to bring a human being as a sacrifice. In the Book of Leviticus, only distinct species of animals are permitted for use in blood sacrifices.
The ancient pagan religions promoted the same idea about atonement as Christians do today (e.g. Molech). They would joyfully offer a child into the fires of their sacrificial offering in order to expiate their sins and appease the gods. Hmmm… why would a child sacrifice be used in this pagan ritual rather than an adult? The reason is because a child is thoroughly innocent of sin. A child, they reasoned, could not have committed sin and therefore mirrored the animal sacrifice which also had to be unblemished
Hosea 14:2-3 states,
Take words with you, and return to the LORD. Say to Him, "Take away all iniquity; receive us graciously, for we will render for bulls the offering of our lips."
No man can atone for the sins of another, each person is accountable for their own works. I believe Ezekiel Chapter 13 mentions that.