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As wrote in Genesis 9:8-11 - The Recipients of God’s Covenant with Noah (Part 2) - Who else was there?, it would seem that most of the modern world did not initially descend from Adam, let alone Noah.  My list was not exhaustive, but according to fossil records, the following major populations of people have been around since before Adam:

China - 67,000 years
India - 30,000 years
Africa - 200,000 years
Native Americans - 16,500 - 40,000 years
Australia - 40,000 years
Middle East - 60,000 years

Adam descended from the Middle Eastern population, after it left Africa.  He lived somewhere around 6,000 to 10,000 …

As described in Genesis 9:8-11 - The Recipients of God’s Covenant with Noah, the recipients of God’s promise to never wipe out all people from a land are Noah and his descendants.  This was not the first time God excluded most of the world from a covenant (Adamic covenant was only with Adam and his descendants, not the rest of the world).  It would not be the last (The Mosaic covenant would only be with the descendants of Isaac).  That said, God reserves the right to graft non-recipients into a covenant, hence making them recipients if He so chooses.  Consider this passage from Romans 11…
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In Genesis 9:1-3 - When did man start eating animals? (Part 1) and Genesis 9:1-3 - When did man start eating animals? (Part 2), I make the assertion that mankind outside Adam and his descendants were eating animals long before Adam was even born.  Adam however was put into a garden, and given plants to eat and animals to care for.  When God cursed the ground, Adam’s descendants sinned further by eating the animals around them.  So, God used Noah to save representative samples of the animals there, killed off the people and remaining animals in their land, and then made the saved animals wild …

There are several arguments to be made, if one is to make the case that Genesis 9:3 is not the beginning of human carnivorism.  Theologically, they include the following:

Though sin can cause death, death is not sin
God’s statements in Genesis 9:1-3 were not a worldwide change
Adam’s descendants were eating meat already

Here is a good post to start with: 

Problems with Interpreting the Flood - Part 4 - Partial Revelation 

I have dealt with #1 at length already.  Here some good posts about it:

Genesis 2 - A recall of Genesis 1? No. …

 1 Then God blessed Noah and his sons, saying to them, “Be fruitful and increase in number and fill the earth. 2 The fear and dread of you will fall upon all the beasts of the earth and all the birds of the air, upon every creature that moves along the ground, and upon all the fish of the sea; they are given into your hands. 3 Everything that lives and moves will be food for you. Just as I gave you the green plants, I now give you everything.
The verses complement the following excerpts in the Creation account:
Genesis 1:
  28 God blessed them and said to them, “Be …

Here are the particulars of God’s promise that he would never again “curse the ground because of man” or “destroy all living creatures”…
 22 “As long as the earth endures,
       seedtime and harvest,
       cold and heat,
       summer and winter,
       day and night
       will never cease.”
It is an interesting promise, because it reiterates God’s promises above, but it is not immediately clear how so.

“Seedtime and harvest, cold and heat, summer and winter, day and night,” are now conditional on the earth enduring.  Enduring what?  Well, the word translated “endures” is “yowm”.  As used, it refers to the remaining designated time of something.  In this case, for the time the earth remains, seedtime and harvest, etc., will never cease.  In …

 13 By the first day of the first month of Noah’s six hundred and first year, the water had dried up from the earth. Noah then removed the covering from the ark and saw that the surface of the ground was dry. 14 By the twenty-seventh day of the second month the earth was completely dry. 
What are the dates in verses 13 and 14 above?  I can tell you what you what they’re not.  Verse 13 is not the date when the water had dried from the earth… it was the latest date at which the water dried from the earth.  And verse 14?  That is the latest date by which the earth was …

 13 By the first day of the first month of Noah’s six hundred and first year, the water had dried up from the earth. Noah then removed the covering from the ark and saw that the surface of the ground was dry. 14 By the twenty-seventh day of the second month the earth was completely dry.
This is a good opportunity to point out an interesting pattern in the flood narrative.  In verse 13, cutoff date for when “the surface of the ground was dry.” It is followed by verse 14, where see cutoff date for when the “the earth was completely dry.”  In Hebrew, “ground” and “earth” are the same word we have been seeing …

In Genesis 8:6-7 - “Is the land dry?”, we saw that Noah used a raven, potentially a fan-tailed raven, to see whether the flooded land had dried.  It would seem that the fan-tailed raven’s habitat was almost exactly the sections of the Middle East and Africa that would have been impacted by a flood overflowed both the Mediterranean and the Red Sea.  This doesn’t mean it rained all that way, just that it was effected enough for the raven to find no dry land 150 days after the floodwaters stopped flowing.  However, just because the land wasn’t dry does not mean the waters had not receded.  So, Noah changed …

 6 After forty days Noah opened the window he had made in the ark 7 and sent out a raven, and it kept flying back and forth until the water had dried up from the earth.
Having spent time developing the argument that Noah built the ark within the mountains of Ararat, away from the general population that was to be destroyed, it starts to paint a picture of Noah’s thought process as he processes what to do after the ark lands.

One of the things that always confused me was why he sent out the birds.  After all, he knew the water outside the ark was going down.  Why wasn’t watching it good enough?  Well, …