The reason Noach’s children were saved.
A Medrash (Yalkut, 43) tells us that Noach noticed that the people of his generation were all evil, and he decided to refrain from having children until the world improved. When he reached the age of 500, he realized that there was a possibility that he would die, leaving behind no children to inhabit and populate the world. The Torah commands a person to ‘be fruitful and multiply’, and a person must have children. When Noach realized this, he made sure to have children. He had no other reason to have children other than to follow Hashem’s precepts and listen to His laws.
Now, the possuk reads אֶּת הָׁא לוקים הִתְהַלֶּךְ נֹחַ . וַיּוֹלֶּד נֹחַ שְׁלשָׁׁה בָׁנִים - Noach saw that he was going with Hashem, i.e. that he would die eventually, and would be left without any children. Therefore, וַיּוֹלֶּד נֹחַ שְׁלשָׁׁה בָׁנִים – Noach gave birth to three children. He had those children solely becuase he wished to serve Hashem. They were also accredite to his merit, with which he survived the Greal Flood.
Alternatively, albeit in the same vein, אֶּת הָׁא לוֹקים הִתְהַלֶּךְ נֹחַ – Noach judged himself (using the Divine trait of דִין – judgement – which is referred to by Hashem’s name of א לוקים) and found himself lacking children. He realized that he had no right to decide not to have children, against the expressed command of Hashem of פְרוּ וּרְ בוּ – be fruitful and multiply. Therefore, וַיּוֹלֶּד נֹחַ שְׁלשָׁׁה בָׁנִים – Noach gave birth to three children.
The Ohr Hachaim adds, based on a Medrash, a reason Noach had not to have children. The Medrash, quoted in Rashi (Bereishis 5:32) says that Noach was fully aware that a Flood was coming, and did not wish to have children and grandchildren. If they would be wicked, they would be destroyed in the Flood, and he preferred not to have descendants, rather than have descendants that would be destroyed. If they would be righteous people, they would require more arks to rescue them, and Hashem would perform multiple miracles to save them. For this reason, Hashem prevented him from having children until he was 500 years old. When his oldest child reached the age of 100, the Flood would begin. The possuk (Yeshaya 65:20) says "לֹא יִהְיֶּה מִשָׁם עוֹד עוּל יָׁמִים וְזָׁקֵן אֲשֶּׁר לֹא יְמַלֵא אֶּת יָׁמָׁיו כִי הַנַעַר בֶּן מֵאָׁה שָׁׁנָׁה יָׁמוּת וְהַחוֹטֶּא בֶּן מֵאָׁה שָׁׁנָׁה יְקֻלָׁל" - "There shall be no longer be an infant who lives but days, or an old man that has not filled his days; for the youngest shall die at one hundred years old, and the sinner being a hundred years old shall be accursed." Prior to the Great Flood, nobody was liable for his sins, at least in the Heavenly reckoning, until the age of 100. Noach’s three children would not have their own reckoning in Heaven, because they were underage.
The possuk is now to read אֶּת הָׁא לוֹקים הִתְהַלֶּךְ נֹחַ – Noach used the Divine method of judgement, and figured out that the time had come for him to have children. He could rest assured that when the judgement day came, and the world was in danger of annihilation, his children and their actions would not be included in that judgement, and would not be destroyed in the flood. Therefore, וַיּוֹלֶּד נֹחַ שְׁלשָׁׁה בָׁנִים – Noach gave birth to three children.
Based on this, the Ohr Hachaim answers his second question too. The reason Noach had these children now was because of his trait of ‘menucha’ calm. He gave birth to a calm group of children, children who would not be destroyed in the flood and would live out their lives in peace. The Torah repeats his name to show us the midah with which he had the children and how they were saved.
The Ohr Hachaim continues, with a deeper explanation, answering his fifth question too. If Noach’s children were to be saved because they were underage, what happened to all of the other people who were underage at the time? Why were the children also destroyed in the Great Flood? They were not liable for Divine judgement either, they should have survived too?
The Ohr Hachaim quotes the possuk later (Bereishis 7:1) וַיֹּאמֶּר ה' לְנֹחַ בֹא אַתָׁה וְכׇל בֵיתְךָ אֶּל הַתֵבָׁה כִי אֹתְךָ רָׁאִיתִי צַדִיק לְפָׁנַי בַדוֹר הַזֶּה - Hashem said to Noach, "Come into the ark, you and your entire household, for it is you whom I have seen to be righteous before Me in this generation." The Ohr Hachaim there explains that Hashem was telling him that the only one who was a true Tzadik, deserving of being saved, was Noach. The others were saved along with him.
This tells us that being underage is insufficient. The underage people were judged based on their parents. If their parents were found guilty and liable for destruction, the children went along with them.
Those whose parents were found righteous and eligible for rescue from the Mabul could bring their children along with them, as well as their children’s wives. All were included in the family of the patriarch, who was deemed righteous. Noach’s children could be included in his rescue.
This is the meaning of the triple-repeated word אֶת, which includes the wives of the children. Noach essentially gave birth to his children’s wives by being the one that saved them from the Divine annihilation that befell the world.
