Our power to rectify the first 6 days of Creation

Lubavitcher Rebbe, Zeh Hayom Techilas Ma'asecha, Erev Rosh Hashana 5742 (Maamorim Melukatim)

To explain the subject more deeply (that Rosh Hashana, the day Adam Harishon was created, is the "beginning of your Divine service (avodah)" [that Adam can fulfill the purpose of Creation]): it is known that the Divine service of a man has the power to change the past.[1] And it is understood from this in relation to the Divine service of Adam Harishon who was the formation of Hashem's hands, that the elevation that he brought about in all the created beings through his declaration "Come, lets us bow down [before Hashem our Creator]" also impacts the reality that existed before his Divine service. That since the intention fo the Creation from the beginning is that the man, through his Divine service, will bring down a revelation of G-dliness in the world, thus, after the revelation of G-dliness is brought down into the world it brings about an elevation also in the reality of the world that existed prior to this, and specifically in that it [the time which preceded this] served as a preparation for the revelation that [ultimately] came about through the Divine service of the man.

This is why the day of Rosh Hashana, the day of the creation of Adam Harishon, is "the beginning of your Divine service", that the simple meaning (and nothing in Torah leaves its simple meaning) of the beginning of your Divine service is the beginning of all the deeds, including the deeds that were done by Hashem in the first days of Creation (including also the time of these days[2]), because the Divine service of Adam Harishon also brought about an elevation and a chiddush in the reality of the world that existed before this, and thus this is the day that is the beginning of your Divine service, the beginning of the entire Creation.

[1] In addition to the fact that he has the ability to change his past -- "If he did tshuva from love he uproots his sin from its beginning" (Rashi, Yoma 86a) -- he also has the ability to change the past that is outside of himself,* like "a sage uproots the oath entirely" (Kesuvos 74b); when the beis din makes a leap year -- the signs of virginity return (Yerushalmi Nedarim 86:8. And more).

[2] Because also "the time itself is...an aspect of new creation, etc." -- Siddur with Chassidus [of the Alter Rebbe] 75d.

* What is relevant here is the change of the past in the things that are outside of him -- see what follows, that through the service of Adam Harishon a change is brought about in the past of the world.

Prophecy will return before Moshiach

Rambam, Igeres Taimon

As a preparatory step for Moshiach's coming... prophecy will return to Israel.

New Torah

Shelah, Parshas Ekev

In the future there will be a new Torah. Not really new, G-d forbid, only that the letters will combine differently -- like it was Above before it was given.

Yissurim (suffering): elevating sparks trapped in impurity

Tzemach Tzedek, Derech Mitzvosecha, Biur Achrei p. 192

The advantage of yissurim (suffering) is that it is capable of refining the three completly impure klipos...because the yissurim come from the "other side" [of evil] thus through them one can refine the good from them.[...] When a man sins, he draws life-force of kedusha into the three impure klipos, and there is no way to elevate these sparks except through yissurim -- when the klipa is given authority over the man in by this the sparks are extracted. In Egypt the miracle was that the sparks were extracted from Above, without the need to endure yissurim under the hands of klipa.

[...]A person is not permitted to act with self-sacrifice on condition that a miracle will be performed from him, because if he sets this condition then no miracle will be performed. The reason for this is that it is impossible to refine [the sparks in the impure klipos] except by allowing the "other side" to have authority over him. Thus, when he sacrifices himself on condition of a miracle this means that he doesn't agree to endure any yissurim from the klipa at all, but when he acts with actual self-sacrifice this indicates that he truly agrees to endure yissurim from the klipa and thus it can happen that a miracle will be performed for him: to break the klipa [and elevate the spark] from Above after only a brief period of submitting to its authority.