There could have been many reasons for early human migration to North America, but one of the more obvious ones is because they were not that well off in their home. Long ago, that might have been caused by climate change. It might have become too cold, or too hot, or too wet, which made life very hard. Climate change also affects food supply. The early humans may have been following a herd across Beringia to North America.
http://www.livescience.com/7640-humans-migrate-americas.html

The first Americans are believed to be Asians, and Native
Americans descend from these first Asian explorers. No doubt, the earliest Americans were rough. Male skeletons showed injuries of often fights, and female skeletons were smaller with signs of malnourishment and domestic abuse. No one is 100% positive on when the first Americans came though. In 1908, a cowboy found the remains of a giant bison that had roamed the continent over 10,000 years ago. Not long after, spear points dating over 13,000 years old were found. Archeologists and researchers might find something older soon. Anyways, the question still is asked. How did the first Americans get here? There are a few theories to answer this question. The first theory is the land bridge between Asia and North America. But, this theory was proven improbable as if people came before the last Ice Age, then the land bridge would not have been revealed. Another theory is they came by boat. This makes more sense, as they could have used boats at the time of when they came. Nonetheless, the first North Americans were Asian Immigrants.
http://ngm.nationalgeographic.com/2015/01/first-americans/hodges-text

Why did the early humans migrate across the Bering Land Bridge all those years ago? There are a few reasons that these events occurred.  For example, climate. Climate was very unstable at this time and life seemed to be a struggle for the people of siberia. No matter what it was, the weather was never the same. This could have caused them to want to immigrate. Another reason would be possible conflict. Conflicts between other tribes or peoples around the Natives could’ve started conflict.  (http://www.livescience.com/7640-humans-migrate-americas.html)

(2 Who were the first Americans?
 Despite the term “Christopher Columbus Discovered America”, the first people to live in the Americas were tribes called Native Americans. However, how they got here is a debatable topic. Some believe that people from the northeast part of Asia used the Bering Land Bridge as a bridge to cross and settle in the Americas. Others believe things along the lines of southeast Asians being the people who came over on the bridge first. (http://news.nationalgeographic.com/news/2003/09/0903_030903_bajaskull.html)