What events allowed for the early settlement of the Americas during the Ice Age?
There is no definitive answer; but there are several theories which could explain this phenomena. The prevailing theory is that since the ice to form the glaciers of the ice age came from the oceans, those bodies of water were of a much shallower depth than now. This allowed for a land bridge to develop between Siberia and Alaska across the present Bering Strait, an area which has been denominated Beringia. This land bridge would have been open for several thousand years during which time humans from Asia migrated while following herds of game animals. Incidentally, it is believed that this same event happened in the Indian Ocean region, allowing population of both Japan and Indonesia.
An intriguing theory has been suggested by C. Vance Haynes, a Geological Archaeologist at the University of Arizona. He has postulated that in a warming period during the last ice age an ice-free corridor opened parallel to the West Coast of the United States. This allowed those people who crossed over Beringia to migrate downward into the Southwestern United States.
New discoveries every day at more to our knowledge of early Americans. It is entirely possible that within the next few years, these theories might be completely disproved.