"And Noah was five hundred years old" (Genesis 5:32). What is the reason that everyone in his generation fathered children at a hundred or two hundred years, while he fathered at five hundred? Rather, the Holy One, blessed be He, said: If they are wicked, I do not wish that they perish in the waters; and if they are righteous, I would burden him to build many arks. So the Holy One, blessed be He, restrained his fountain and he fathered children at five hundred, so that even Japheth, the eldest, when the Flood came, would not yet be a hundred years old and liable to punishment. "And Noah fathered Shem." But was not Japheth the eldest? Rather, you first expound Shem because he was righteous, because he was born circumcised, because the Holy One, blessed be He, set His Name upon him, because Abraham came forth from him, because he served in the high priesthood, because the Temple was built within his territory. And the number of his letters the Holy One, blessed be He, suspended for the generations from the generation of the Flood until the generation of the Dispersion: three hundred and forty years. "And it came to pass, when men began to multiply" (Genesis 6:1). This teaches that they were spilling their seed upon the trees and upon the stones; and because they were steeped in fornication, the Holy One, blessed be He, increased females among them, as it is written, "and daughters were born to them." Rabbi Shimon son of Rabbi: his wife bore him a daughter. Rabbi Hiyya the Elder saw him and said to him, "The Holy One, blessed be He, has begun to bless you." He said to him, "How so?" He said, "As it is written, 'And it came to pass, when men began to multiply,' and so on [where multiplying is linked to daughters]." He went up to his father, who said to him, "The Babylonian has gladdened you. Even so, there is need for wine and need for vinegar; the need for wine is greater than for vinegar. There is need for wheat and need for barley; the need for wheat is greater than for barley. When a man marries off his daughter and lays out his expenses, he says to her, 'May you have no need to return here.'" Rabban Gamliel married off his daughter. She said to him, "Father, pray for me." He said to her, "May you have no need to return here." She bore a male child. She said to him, "Father, pray for me." He said to her, "May the cry of 'woe' never cease from your mouth." She said to him, "Father, at the two joys that have come to me you curse me?" He said to her, "Both are blessings. Since you will be at peace in your house: may you have no need to return here. And since you have a living blessed child: may the cry of woe never cease from your mouth, the woe of 'my child has not eaten,' the woe of 'my child has not drunk,' the woe of 'my child has not gone to the synagogue.'"
Why Noah Did Not Father Children Until He Was Five Hundred
Yalkut Shimoni on Torah 43:2
וַיְהִי נֹחַ בֶּן חֲמֵשׁ מֵאוֹת שָׁנָה. מַה טַעַם כָּל דּוֹרוֹ מוֹלִיד לְמֵאָה וּלְמָאתַיִם, וְהוּא מוֹלִיד לַחֲמֵשׁ מֵאוֹת שָׁנָה, אֶלָּא אָמַר הַקָּדוֹשׁ בָּרוּךְ הוּא, אִם רְשָׁעִים הֵן אֵין רְצוֹנִי שֶׁיֹּאבְדוּ בַּמַיִם, וְאִם צַדִּיקִים הֵן אַטְרִיחַ עָלָיו וְיַעֲשֶׂה תֵּבוֹת הַרְבֵּה, וְכָבַשׁ הַקָּדוֹשׁ בָּרוּךְ הוּא מַעַיָנוֹ וְהוֹלִיד לַחֲמֵשׁ מֵאוֹת שָׁנָה, שֶׁאֲפִלּוּ יֶפֶת שֶׁהוּא גָּדוֹל לִכְשֶׁיָּבֹא הַמַּבּוּל אֵינוֹ בֶּן מֵאָה שָׁנָה לָעֹנְשִׁין. וַיּוֹלֶד נֹחַ אֶת שֵׁם. וַהֲלֹא יֶפֶת הוּא הַגָּדוֹל, אֶלָּא בִּתְחִלָּה אַתָּה דּוֹרֵשׁ שֶׁהוּא צַדִּיק וְשֶׁנּוֹלַד מָהוּל, וְשֶׁיִּחֵד הַקָּדוֹשׁ בָּרוּךְ הוּא שְׁמוֹ עָלָיו וְאַבְרָהָם יוֹצֵא מִמֶּנּוּ, וְשֶׁשִּׁמֵּשׁ בִּכְהֻנָּה גְּדוֹלָה וְשֶׁנִּבְנָה בֵּית הַמִּקְדָּשׁ בִּתְחוּמוֹ, וּמִנְיָן אוֹתִיּוֹתָיו תָּלָה הַקָּדוֹשׁ בָּרוּךְ הוּא לְדוֹרוֹת מִן דּוֹר הַמַּבּוּל עַד דּוֹר הַפְּלָגָה שְׁלֹשׁ מֵאוֹת וְאַרְבָּעִים שָׁנָה. (בראשית ו א) וַיְהִי כִּי הֵחֵל הָאָדָם לָרֹב. מְלַמֵּד שֶׁהָיוּ שׁוֹפְכִין אֶת זַרְעָם עַל הָעֵצִים וְעַל הָאֲבָנִים וּלְפִי שֶׁהָיוּ שְׁטוּפִין בִּזְנוּת, רִבָּה לָהֶן הַקָּדוֹשׁ בָּרוּךְ הוּא בִּנְקֵבוֹת. דִּכְתִיב וּבָנוֹת יֻלְּדוּ (לָהֶן) [לָהֶם]. רַבִּי שִׁמְעוֹן בְּרַבִּי יָלְדָה לוֹ אִשְׁתּוֹ נְקֵבָה. חַמְתֵיהּ רַבִּי חִיָּא רַבָּה, אָמַר לוֹ, הִתְחִיל הַקָּדוֹשׁ בָּרוּךְ הוּא לְבָרֶכְךָ. אָמַר לוֹ, מַה הֵן אָמַר לוֹ, דִּכְתִיב וַיְהִי כִּי הֵחֵל הָאָדָם לָרֹב וְגוֹ'. עָלָה אֵצֶל אָבִיו אָמַר לוֹ, שִׂמַחֲךָ הַבַּבְלִי אַף עַל פִּי כֵן צֹרֶךְ לְיַיִן וְצֹרֶךְ לַחֹמֶץ, צֹרֶךְ לְיַיִן יוֹתֵר מֵחֹמֶץ צֹרֶךְ לְחִטִּין וְצוֹרֶךְ לִשְׂעוֹרִין, צֹרֶךְ לְחִטִּין יוֹתֵר מִן הַשְׂעוֹרִין. מִשֶּׁאָדָם מַשִּׂיא אֶת בִּתּוֹ וּמוֹצִיא אֶת יְצִיאוֹתָיו הוּא אוֹמֵר לָהּ לָא יְהֵא לְךְ מַחְזוּרִי לְהָכָא רַבָּן גַמְלִיאֵל אַסִיב בְּרַתֵּיהּ. אָמְרָה לֵיהּ, אַבָּא, צַלִּי עָלָי אָמַר לָהּ, לֹא יְהֵא לָךְ מַחְזוּרִי לְהָכָא יָלְדָה בֵּן זָכָר, אָמְרָה לֵיהּ, אַבָּא צַלִּי עָלַי. אָמַר לָהּ, לָא יִשְׁלֶה וַי מִפּוּמָךְ אָמְרָה לֵיהּ, אַבָּא בִּשְׁתֵּי שְׂמָחוֹת שֶׁבָּאוּ לִי אַתְּ מְקַלְּלֵנִי. אָמַר לָהּ, תַּרְוֵיהוֹן צַלְיָן אִנּוּן מִן גּוֹ דְּאַתְּ הֲוְיָא שָׁלֵם בְּבֵיתֵךְ לָא יְהֵא לָךְ מַחְזוּרִי לְהָכָא וּמִן גּוֹ דַּהֲוֵי בְּרִיךְ קַיָּם לָא יִשְׁלֶה וַי מִן פּוּמָךְ וַי דְּלֹא אָכַל בְּרִי, וַי דְלָא שְׁתִי בְּרִי, וַי דְּלָא אָזִיל בְּרִי לְבֵי כְּנִשְׁתָּא.