I disagree, Chaim. It is Christianity which teaches that sincere repentance is not accepted and you need Jesus. You can ask the victim's soul for forgiveness and you can bring the victim back to life with reincarnation and resurrection.
It is the church which sold "indulgences" for
any sin, not Judaism. Did one necessarily require Jesus for the allowance? No. You only needed to pay someone who was recognized as an authority by the church. Christianity will try and muddy the waters of debate on what exactly an "indulgence" was. But the fact is, at its very common denominator, it was payment for permission to commit a sin, and even if that's not what its original intention was, that's what it became, and it was approved by the Church even in its final form. And the only reason why they curtailed it is because it's embarrassing to them.
Cain was an intentional murderer. But God came to him and said to him, "if you will improve yourself, you will be forgiven" (Genesis 4:7). As an eternal lesson for all generations, God instructed Cain about the ability to repent, which is in the hands of every person: to repent and return to God at any time one desires and makes the decision to do so, and God will forgive him.
Do I need to point out the obvious that verse 7 in Chapter 4 comes
before the next verse in which Cain murders Abel? G-D is telling Cain in verse 7 to improve
himself and if he does he will be successful. Cain was born with bad ethical faculties (I drew this inference from Ibn Ezra on this verse, who states that Cain committed sins), Abel had good ethical faculties.
I won't go into great detail, but the Student states that those born with bad ethical faculties "die young" and are "...cast out from the midst of man". But Judaism is not Calvinist Christianity (lehavdil elef havdalot) and we do not believe in predeterminism. Even one who is "cast out" (i.e. born with bad ethical faculties) is told by G-D to try hard. What precisely the mechanism of salvation is for such a person is beyond our knowledge. In medieval times, Jews adopted the theory of the "gilgul" (transmigration of souls). Not everyone accepts this theory, and this is beyond the scope of this discussion.
To conclude, G-D is not forgiving Cain for the sin, to the contrary, G-D goes on to curse him in the following verses.
Out of respect for Chaim I have held back my acerbic disposition and my acid tongue in my refutation, but please study your sources carefully next time before writing blindly.