Do native americans have asian roots?

They're from Siberia, "Siberian-Americans" would be a more accurate name. Because they aren't native to North America either.

The Far East Siberian Chukotka/Yupik people and the Alaskan Chukotka/Yupik are “the same”, I think the same is said for most Eskimo/Aleut peoples.

There is Mongol (Asian) influence around southern Russia and what you would call “Eskimo” around the northern Arctic Circle. It helps to look at a globe rather than a flat map to realize how close Alaskans, Canadians, Russians, and northern Nordic, folks really are.
Also helps to remember the ‘Beringia’ geological mass, or the ancient “Land Bridge” connection between modern Alaska and Russia.

It’s a bit too modern to consider Northern Circle folks as Asian or non, because a vast majority of the ethnic history of the people was based so heavily on geography and what was evolutionarily needed for survival in a very harsh climate. Sturdy folk with puffy faces and thin eyes is an arctic trait, had less to do with political borders.

I grew up north of the Arctic Circle in Murmansk, a far West North Seaport city, my mother was of partial Mansi descent, which is an ethnically Ugric indigenous group. She was blonde hair blue eye as most “mixed” Russians are now, with heavy Slavic influence. But if you look at photos of ethnically Mansi people, barring the mixed ones, you’ll see they look almost identical to what you’d consider “Eskimo” in the Americas.

No clue about the deep-red skinned, tall, plains native Americans, I don’t know their history.
Long-winded. But yes, human history would say that northern Native Americans did at some point migrate through Asia, and probably picked up traits as they went.

At what point does ancestry make you asian? Using that logic we are all africans.

Finnish people are about as close as you can be to Asian without being asian by ancestry and migration. A big loop around asia and then settling in one of the most inhospitable bosoms of the world.

The current "native Americans" do. According to scientists they came down from Russia through Alaska when it was still connected and they went south. As they went south the people who were here before them "the clovis people" also fled south all the way to south America. Some people think they fled from the ones coming from Russia. The ones from Russia have more asian in them than the clovis people. The clovis people still live in the Amazon today uncontacted.