Yes, there is doubt that the Hebrews/Jews viewed sacrifice in the same way that evolved in Christianity. The purpose of the blood in the Day of Atonement was to cleanse the sanctuary of sins that had already been transferred from the penitent sinner.
Under the Jews' dispensation, was blood always required for a sinner to be forgiven?
Further to my thoughts that the NT's soteriological fulfilment related to the festivals of Tishri (September/October) rather than Passover at Nisan (March/April), I find support in the NT book of Hebrews. Its metaphors such as "the high priest entering once with blood" relate to Tishri's Day of Atonement.
It is my highly speculative hypothesis that the primitive Church found it advantageous to absorb existing pagan/gentile Spring festivals and to distance themselves from the Jews and their concentrated list of religious observances during Tishri (Autumn - September/October).
Doug