The history of North America up to 1500 AD is a story of a continent that started out empty and gradually got more and more crowded. Probably the first people to come to North America came from East Asia, about 20,000 BC, and then small groups of people kept crossing from time to time. DNA analysis shows that some of these people were related to the first people who left Africa, the people who settled in Australia and New Guinea. Others were descended from East Asians who married Yamnaya, or proto-Indo-Europeans.
Some people came over on a land bridge, with their dogs. They may have been following woolly mammoths that they were hunting for food. The people probably didn’t even realize they had crossed over to North America. Other people probably came from East Asia in small boats, crossing the Pacific Ocean by following the coast around by Alaska. Maybe these people were following the salmon they ate. We don’t know when that happened, but people were definitely catching salmon in Alaska by 11,500 BC.
There’s no archaeological evidence for either method, walking or in boats, but people did get here somehow from East Asia, because we have archaeological traces of people that scientists can date to about 12,000 BC, or even earlier.
(This is what most archaeologists think. Some of the people whose ancestors lived in North America, like the Navajo and the Sioux, tell a different story about their own origins, which you can see here).