Praise be to Allah.
The clear text of the Qur’an indicates that everyone who was on earth drowned in the flood, and no humans or animals were saved except those whom Nooh took with him on board the ark.
Allah, may He be exalted, said (interpretation of the meaning):
“And We saved him and those with him in the laden ship.
Then We drowned the rest (disbelievers) thereafter”
“(So it was) till then there came Our Command and the oven gushed forth (water like fountains from the earth). We said: ‘Embark therein, of each kind two (male and female), and your family, except him against whom the Word has already gone forth, and those who believe. And none believed with him, except a few.’”
“They denied him, but We delivered him, and those with him in the ship, and We made them generations replacing one after another, while We drowned those who belied Our Ayat (proofs, evidences, lessons, signs, revelations, etc.). Then see what was the end of those who were warned”
The Qur’anic text also indicates that the earth was only populated after that by the descendants of Nooh (peace be upon him). As for the believers who were saved with him in the ark, none of their descendants were left. So all the people on earth now are descended from Nooh (peace be upon him).
Allah, may He be exalted, says (interpretation of the meaning):
“And indeed Nooh (Noah) invoked Us, and We are the Best of those who answer (the request).
And We rescued him and his family from the great distress (i.e. drowning),
And, his progeny, them We made the survivors (i.e. Shem, Ham and Japheth).
And left for him (a goodly remembrance) among generations to come in later times.
Salamun (peace) be upon Nooh (Noah) (from Us) among the Alameen (mankind, jinns and all that exists)!"
Verily, thus We reward the Muhsinoon (good-doers)
Verily, he (Nooh (Noah) ) was one of Our believing slaves.
Then We drowned the other (disbelievers and polytheists, etc.)”
‘Ali ibn Abi Talhah narrated from Ibn ‘Abbaas: There was no one left except the progeny of Nooh (peace be upon him).
Qataadah said concerning the words “And, his progeny, them We made the survivors”: All people are among the progeny of Nooh (peace be upon him).
Tafseer al-Qur’an al-‘Azeem by Ibn Katheer, 7/22
Al-Haafiz Ibn Katheer (may Allah have mercy on him) said:
The scholars differed concerning the number of people who were with him on board the Ark.
It was narrated from Ibn ‘Abbaas (may Allah be pleased with him): There were eighty men, accompanied by their wives. It was narrated from Ka‘b al-Ahbaar that there were seventy-two people. It was also said that there were ten people.
A number of the commentators said: The water rose until it was fifteen cubits above the top of the highest mountain on earth. This is the view of the People of the Book. It was also suggested that it was eighty cubits, and that it covered the length and breadth of the earth, plains, rugged terrain, mountains, desolate regions and sandy deserts, and there was no one left of those who had been living on earth at all, neither young nor old.
Imam Maalik said, narrating from Zayd ibn Aslam: The population at that time filled the plains and mountains…
Allah did not give any of those believers who were with him children or descendants, apart from Nooh (peace be upon him). Allah, may He be exalted, says (interpretation of the meaning): “And, his progeny, them We made the survivors” [as-Saaffaat 37:77]. So everyone on the face of the earth today, of all races, are the sons of Adam who are descended from the three sons of Nooh, namely Saam, Haam and Yaafith (Shem, Ham and Japeth). End quote.
Al-Bidaayah wa’n-Nihaayah, 1/111-114
Al-‘Allaamah at-Taahir ibn ‘Ashoor (may Allah have mercy on him) said: The fact that the phrase “them We made the survivors” begins with the pronoun is to indicate exclusivity. In other words: There was no one left of mankind except those whom Allah saved with Nooh in the ark, of his offspring, then those who were descended from them. There was no one left of the sons of Adam apart from the progeny of Nooh. So all nations are among the progeny of the three sons of Nooh. The apparent meaning of this is that those who believed with Nooh apart from his sons did not have any offspring. Ibn ‘Abbaas said: When Nooh came out of the ark, the men and women who were with him died, except for his sons and his wives. Thus we may respond to the apparent contradiction between this verse and the verse in Soorat Hood (“We said: ‘Embark therein, of each kind two (male and female), and your family, except him against whom the Word has already gone forth, and those who believe. And none believed with him, except a few.’” [Hood 11:40]). This is based on the idea that the flood covered the entire earth and destroyed all humans except those whom Nooh carried on board the Ark. End quote.
At-Tahreer wa’t-Tanweer, 23/47
With regard to the words of Allah, may He be exalted, (interpretation of the meaning):
“ ‘O offspring of those whom We carried (in the ship) with Nooh (Noah)! Verily, he was a grateful slave’”
“Those were they unto whom Allah bestowed His Grace from among the Prophets, of the offspring of Adam, and of those whom We carried (in the ship) with Nooh (Noah), and of the offspring of Ibrahim (Abraham) and Israel and from among those whom We guided and chose. When the Verses of the Most Beneficent (Allah) were recited unto them, they fell down prostrating and weeping”
These words do not indicate that the offspring of the believers whom Nooh (peace be upon him) carried with him survived; rather what is meant is the sons of Nooh (peace be upon him) whose progeny survived, not the other believers.
Al-‘Allaamah al-Ameen ash-Shanqeeti (may Allah have mercy on him) said: The verse “‘O offspring of those whom We carried (in the ship) with Nooh (Noah)! Verily, he was a grateful slave’”[al-Isra’ 17:3] states that none of the offspring of those who were carried on the ark with Nooh survived, apart from the offspring of Nooh, as it says in the verse: “And, his progeny, them We made the survivors” [as-Saaffaat 37:77]. End quote.
Adwa’ al-Bayaan, 3/13
And Allah knows best.