How are sins forgiven in the Torah?
Ezekiel 18:21-23 gives a succinct answer to your question:
"It may be that a wicked man gives up his sinful ways and keeps all my laws, doing what is just and right. That man shall live; he shall not die. None of the offenses he has committed shall be remembered against him; he shall live because of his righteous deeds. Have I any desire, says the Lord G-d, for the death of a wicked man? Would I not rather that he should mend his ways and live?"
So sincere REPENTANCE for misdeeds is how Jews are forgiven. When the Temple stood, Jews brought sacrifices to repent for sin. But if they also did not have sincere repentance, their sacrifice meant nothing.