No, no, yes.
America is ASB. At least two major migrations seem to have occurred over the Bering in the past few thousand years and there were almost definitely many more. On top of that you have the Norse in the northeast and the Polynesians in the southwest, plus whatever small-scale or undocumented migrations.
Australia is also ASB. There's the first landing of the Australians a few tens of thousands of years ago, which was likely planned and not an accident. Some Indians migrated a few thousand years ago. The Macassan connection is extremely well-documented, and although the Macassans postdate European "discovery" there we have the baijini, who, if they existed, predated the Europeans in the Yolngu country. Again add to that whatever small-scale or undocumented migrations.
New Zealand, by contrast, is possible if things go terribly for a lot of Polynesians.