Contrary to the understanding of many, the covenant established with God’s chosen race was potentially do-able; moral perfection was not expected; provision being made for human weakness through the system of animal sacrifices. Such sacrifices were only a figure of the Eucharist to be established under the Covenant of Christ’s Blood, but the blood of bulls and goats DID expiate the day to day inadvertent sin of God’s people (e.g. Lev16:15-22), which is why Yahweh commanded them to perform them:
“If through inadvertence you fail in any of the orders which Yahweh has given to Moses… this is what must be done: If it is an advertence on the part of the community, the community as a whole will offer a young bull as a burnt offering as a smell pleasing to Yahweh with the prescribed accompanying cereal offering and libation and a he-goat AS A SACRIFICE FOR SIN. The priest will perform the rite of expiation for the entire community of Israelites AND THEY WILL BE FORGIVEN for it is an inadvertence (Num15:22-25)
On the other hand those who sinned wilfully would be treated as aliens and “bear the consequences of their guilt” (v31). So moving forward in time to some of Paul’s polemics it was not the case that Jews believed they had perfectly to “keep Torah” in order to be accepted by God; forgiveness for day-to-day sins was provided. Neither was it their “human initiative” or “pride” to endeavour to keep the Law (a la Augustine/Luther/Calvin) but a response to divine teaching; indeed Yahweh wished they had tried all the harder to honour their side of the Covenant (Ex19:5,6).
“But what about the teaching of Hebrews?” some are bound to ask. The writer to the Hebrews was not contradicting the above. He taught that although bulls’ and goats’ blood could purify the flesh (Heb9:13), it could not sanctify the soul by taking away sin (Greek:“aphairein”) and thereby cleanse the conscience (Heb9:13-14). Pardon for sin is one thing; cleansing from sinfulness is quite another; this has been a major area of confusion for many. The shedding of an animals’ blood under the Old Covenant enabled sin to be pardoned as we have just observed from the Pentateuch but it did nothing to progress the partaker towards moral rectitude (Heb10:1).  The Old Law made no one perfect (Heb7:19); only the blood of Christ can “save to the uttermost” (Heb7:25) by “purging the conscience of dead works so as to serve the living God” (Heb9:14).
PS. I am putting  out a number of tweets summarising the background to these blogs and the book they complement – HERE