When did the native American arrive in the Americas?

We can not currently know the answer to that question unless someone invents a time machine over the next few days. Some historians believe that the migrations took place between 12,000 and 16,000 years ago; the earliest human remains found in the Americas may indicate a colonisation from Asia happening about 27,000 years ago. Recent finds might push this back further to as much as 40,000 years ago. Finds along the Savanagh River in Georgia may date to before 40,000 years ago.

Since more archaeological finds are being made and dated througouht the Americas all the time, our current knowledge of this subject is very far from complete. Stick around for the next 500 years and we may know the answer.