You have stumbled onto a topic of great controversy in archaeological communities. DNA evidence suggests that people indigenous to North and South share common ancestry. However, how the ancestors got to the Americas is more debated.
The Land Bridge from Asia
As more sites are discovered with later and later dates, the Land Bridge as the first wave of colonization has been widely considered untrue. While people likely did take Beringia, as it is called, by following the game, that ice free corridor that would have let the game down from Alaska into the continental US wouldn't have opened until after the Clovis tool complex became widespread 1200 years ago.
The Chicken
There are Polynesian chicken remains in Chile. Let that sink in. A bird from India crossed the Pacific, the largest, ocean to get to the Americas before Europeans. This suggests at least occasional trade with Polynesian peoples. This could mean that some ancient Polynesians, who were master navigators and sailors, settled in the Americas the same way the settled most islands in the Pacific.
Other Boats
There is a site in Idaho, US called Cooper's Ferry where stone tools that looked similar to contemporary tools used in Japan. More island people's who are good at boat. It would have been possible for short range boats to follow a coastline around Beringia into the Americas. A long range boat could have gone straight across, though evidence for those types of boats is disputed.
Most experts agree that there were multiple waves of migration, but genetic evidence suggests that all of them originated in Central Asia before migrating out. So, you are in a technical sense "Native American", though using it as a descriptor would be confusing, so I don't recommend using it. My understanding is most people in your situation would call themselves Indigenous.
