Rashi takes care to carefully document all the dates surrounding the flood, (*Mei Noach), and we find that this event (which again is a symbol for peace on earth brought by the Mashiach) took place on the 25th of Elul.
[…] Did anything else that was significant happen on that same date? Indeed it did! The 25th of Elul is actually the first day of creation. Rosh Hashanah, the 1st day of Tishrei, is the 6th day of creation
[…] In Hebrew, the words for "world" and "eternity" are identical. So the phrase שלום עולם can be translated as either “world peace” or “eternal peace.”
[…] What other significant event occurred in the Tanach on that day? The 24th day of Elul was the day on which David sinned with Batsheva. This sin had three very severe elements in it: adultery (even though it wasn't a hundred-percent adultery), idolatry, and murder. (full discussion in the link below, and David was forgiven by G–d)
[… If] you read the Torah, it's written that David took Batsheva towards the evening, which equals 777, the number of our … year). This is the same ( לעת הערב phrase used (for the first time in the Bible) when the dove returns with the olive leaf in its beak. If David took her at late afternoon, towards the evening, it was already the night of the 25th that they sinned, or perhaps the Zohar means that he took her on the late part of the 23rd of Elul and the sin itself occurred on the 24th. In any case, the 24th of Elul, the day before the creation (of light), represents total, primordial darkness (as does the night of the 25th of Elul, the darkness of the first night of creation that preceded the light of the morning).
[…] There are again three things that occurred on the 25th of Elul, the creation of the world, the return of the dove, and the sin of King David (the origin of the Mashiach). David's teshuvah is the elevation of the bitterness and the transformation of darkness into light.
[…] In the Talmud, it was Rabbi Yehoshua ben Levi who asked this question, and heard the Mashiach replying, "today!" Elijah explained to him that there is a condition—if you listen to God's words.
From: 5777 Year of the Dove, Olive Branch and World Peace by Rabbi Yitzchak Ginsburgh shlit”a.