This is something that is not yet known for sure. There is a great deal of controversy still among anthropologists and archaeologists on this topic.
It had once been thought that there was conclusive evidence that the ancestors of the Native Americans had come into the Americas about 12,000 years ago. This was the "Clovis First" theory. However, there is now significant doubt about this theory. There are sites as far south as Chile that seem to indicate that Native Americans had gotten that far 12,500 years ago. This would mean that they would have had to have gotten into the Americas quite a bit before that (in order to get that far south by 12,500 years ago).
This may mean that the ancestors of the Native Americans got to the Americas as long ago as 16,000 years ago. There are those who believe that people got to the Americas as much as 40,000 years ago, but this is still very controversial.
Overall, there is so much controversy about this topic that it would be wise for you to check your book or your lecture notes to see which theory your instructor subscribes to.
just watched something on the discovery channel that dates the Indians to around 16,000 yrs ago. However, recent skeletal findings indicate humans unrelated to the Indians were here before the Indians, dating as far back as 30,000 yrs. I know I will catch some flack on this, but that is what the information they showed was leading to. They said their was a huge reed forest along the coastal waters and it may have provided a pathway for others prior. Allowing them access to the land south of the ice sheets during the ice age of that period
I hope they prove Indians were not the first ones here, then you all can eat crow with them