If God really did flood the Earth, then aren't we all descendants of Noah's family?

Bible story goes that the Earth was flooded, but Noah was forewarned, so he and his family were safely aboard the ark during said genocidal flood. Assuming the flood lasted long enough to kill off all the other humans, wouldn't that make all of us descendants of Noah's family? That means sooner or later... show more Bible story goes that the Earth was flooded, but Noah was forewarned, so he and his family were safely aboard the ark during said genocidal flood. Assuming the flood lasted long enough to kill off all the other humans, wouldn't that make all of us descendants of Noah's family? That means sooner or later inbreeding and same-family intermarrying would've taken place since there were no more people.
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