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While the judgment is recorded on Rosh Ha-shana, it is not sealed until Yom Kippur. Therefore, repentance is most appropriate during the days in between.
However, the way the judgment will be carried out is only decided on Hoshana Rabba and Shemini Atzeret (at the end of Sukkot), so it is still possible to improve things before then. And even afterwards, as long as the judgment has not yet been put into effect, we can change how it transpires. This can be compared to a country’s budget. Even though the budget is passed at the beginning of the year and the government does not have the authority to change it, every minister has the ability to influence how his or her ministry’s budget will be divided. Even ministry bureaucrats have some leeway in how to direct the budget. Similarly, our Sages tell us the deeds we do all year can influence the Rosh Ha-shana judgment for better or for worse. The Talmud (Rosh Ha-shana 17b) elaborates:
What is an example of “for better”? Let us say the Jews were completely wicked on Rosh Ha-shana, and so were allotted only a small amount of rain. Later, they repented. It is not possible for more rain to fall, as the amount has already been determined. Nevertheless, God can make sure rain falls at ideal times and in places that need it most. (This way, a minimal amount of rain can still bring great blessing.)
What is an example of “for worse”? Let us say the Jews were completely righteous on Rosh Ha-shana, and were allotted a lot of rain. Later, they sinned. It is not possible for less rain to fall, as the amount has already been determined. Nevertheless, God can make sure rain falls at inappropriate times and in places that do not need it (hence, the Jews would derive no benefit from the rain).
Sometimes, if repentance is particularly sincere, it may even change the judgment itself.
