[EinNYC]

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.

[Jamestown1630]

"Come now, and let us reason together, saith the Lord: though your sins be as scarlet, they shall be as white as snow; though they be red like crimson, they shall be as wool."

[Bodleian_Girl]

If the Jew can pay for their own sin by their own work of repenting, why do they need the blood sacrifice?