I have a few theories:
1) They crossed over the Bering Strait land bridge from Seberia (Eastern Russia) during the Ice Age to the Americas when the polar ice caps trapped lots of water, thus making a giant land bridge possible to cross.
2) As you said for Australian DNA, island holping might've been a way. Since, if I remember correctly, they crossed over when the Earth was in an Ice Age with the polar ice caps trapping lots of water than today, so I assume the water levels were lower, thus it might've been easy to sail from island to island in the Pacific on boat a posibility.
3) There have been Clovis spear points found in some West Coast states, whom have also been in western European countries and look very alike and crafted very similarly, so the first Americans might've been European or East Asians that crossed throughout the Silk Road into Europe and somehow made it East Coast of the United States. After all, there have been some supposely skulls (with radio carbon dating) older than the first Americans that came from Eastern Asia, whom resemble Caucasiod features (narrow nose bridge, cliff chin, and such). I can't remember what archeologist named it, but I think it was given a name that starts with a "K" and has "man" in the name.
4) Sailing along the Bering Strait land bridge's shore all the way to the west of Northern America.
5) I highly doubt this is one, but maybe they might've walked vertically throughout the North Pole from East Asia into Northern America in Canada.