Did the WASP's ancestors first settle the western hemisphere?

No, they did not.

The term "Native Americans" refers to the hundreds of societies -- including the Aleuts, Cherokee, Zuni, Sioux, Mohawk, Aztec and Inca -- who first settled the Western Hemisphere.

Some 30,000 years before Christopher Columbus landed in the America's, migrating peoples crossed a land bridge from Asia to North America where the Bering Straight (off the coast of Alaska) lies today. Gradually, they spread throughout North and South America.

Source: Pearson: Society the basics 11th edition, John J. Macionis, Kenyon College