Another interpretation of "after the seven days" (Genesis 7:10): it teaches that He set for them a short span of time after a long span of time.
A Short Deadline Set After a Long One
Yalkut Shimoni on Torah 56:3
דָּבָר אַחֵר, לְשִׁבְעַת הַיָּמִים מְלַמֵּד שֶׁקָּבַע לָהֶן זְמַן קָטָן אַחַר זְמַן גָּדוֹל.