How was the far west settled?

How was the far west settled?
There are for the most part two far wests. The United States is the far west on a global stage that was found, as well as some Pacific Islands, in searching for ways to trade routes to India from Europe but was settled to escape religious prosecution as well as other forms of prosecution.
The far west of the United States was explored by Louis and Clark who were set out on an expedition by the current president of the time Thomas Jefferson, who had just recently bought the Louisiana Territory from France. And Jefferson wanted Louis and Clark to see if they could find a way to the Pacific Ocean for possible trade routes to Asia and he also wanted them to claim any additional land the United States of America's property. They found a way to the Pacific Ocean but they couldn't do it all by boat. The west later became inhabited by people looking for land so they could farm and make a living and later became more populated by the famous Gold Rush.
Scholars still don't know today how those islands or the Americas were settled by its original native people some theories include the Ice Age, and the Land Bridge between Russia and Alaska but all we can do in history is guess at this point.