They could have crossed the Pacific by boat, or got blown across it under the right circumstances. It's true that just about everybody who got pushed away from land and into the ocean by a storm would perish, but some could have survived. After all, people made it to Hawaii in the middle of the Pacific, and there is simply no other way to get to those islands than by boat.

Remember also that possible arrivals had tens of thousands of years in which to make the trip. That's a long time, and if any single surviving, viable group made the jump then humanity would gain a foothold in the new world. It just had to happen once.

I guess the land bridge is possible, but... I don't think people get just how rugged that region is. If you ever take a flight from Beijing to the west coast, just look down as you pass over Northeast China and then Northeastern Russia. It's mostly just snow covered mountains without trees and a lot of frozen lakes. Even if you crossed it very slowly, I'm not sure there's anything at all down there that could sustain a wandering tribe. It just looks like Death to me.

And that's today. Imagine trying to cross during the ice age!