I accept the literal 6, 24 hour day creation of the Earth. So therefore, I also accept that the flood was worldwide. There is even proof on the Grand Canyon that the WHOLE WORLD was flooded during the flood by the shape of the Canyons. The shape looks like they were washed and submerged with water.
But there is still an interesting question now that it's Columbus Day. If literally EVERYBODY ALL PER TE WORLD, except Noah and his family, drowned in the Flood, then how could there be living human beings on the Americas between the time of the Flood and the time of Leif Erickson's arrival into Canada?
Relatively simple.
Noah and Flood was about 4,000 - 4,500 years ago [2480 BC - 1980 BC] if you hold to a young earth via genealogies in the Bible. The Tower of Babel was about 100 or so years after the Flood.
After the people were scattered from Babel, God "scattered" them across the world as was the plan in the first place that they refused - this was done via migration as can be observed and proved.
I looked at a few estimation charts of world populations across the timeline of human history. Some of them vary - but an average said around 2,500 BC there were somewhere around 20 million people and by the time of the 1400's AD - there were around 350 to 375 million. And the human population began to skyrocket from there to today. This was not a religious chart, but a secular one.
Historical Estimates of World Population
The time between Noah's Ark and the early European discoveries of the Americas was about 3,900 years.
The Bible said the people began to scatter across the world. We know that Native Americans in both North and South America came from Asia either across the Bering Strait or along the coastline depending on your acceptance of data. They followed the food in those days. Don't forget that animals came, too. They, then came down via today's Canada into today's United States and down, down into today's Mexico and South America.
I live in Louisiana and we have concrete evidence that people and Wooley Mammoths were here very early. Our earliest people groups were in Poverty Point around 3,400 years ago [1480 BC]. Poverty Point Native Americans ate a lot of fish, frogs, alligators, deer, and more. They were thriving here by that time.
This type of migration to the Americas - the LONG way around [instead of across the Atlantic] - didn't NEED thousands of years to take place. This was done hundreds of year - not thousands.