People arrived in the Americas about 13-15000 years ago from what I've seen. Presumably, this means there were already other civilizations in existence that they had migrated from. I assume these civilizations continued to exist after the emigration of some of them to America, and it seems like they would know that their kin had emigrated to the next continent over. So at what point did the knowledge of the people who'd been living there get forgotten to the point where no one remembered the continent existed?
I can't provide a good answer for your question, because it's based on a misunderstanding of how the migration worked. The movement from Siberia, across the land bridge, into modern-day Alaska, started 25,000 years ago. But they didn't actually make it into North America until 17,000 years ago. (More reading on the migration.)
Remember that the very first writing system only appeared about 5,000 years ago. That's super ancient for us today - we only have the barest sketches of information, and that's only because they did develop writing systems to pass information on. (More reading on early writing.)
So for there to have been a 7,000 year gap between leaving your old friends, and arriving on the "next continent over" - nobody there had any idea. They left thousands of years previously - a bigger difference than between now and the Bronze Age. As soon as they started migrating, there was no way to communicate back - so you have people moving very slowly, over thousands of years. The descendants of the people moving had no idea there was anybody "back home" to tell anything to. The descendants of the people who stayed may have had oral history of "the people who left us" but they had no way to know what happened to them.
So they never knew about the Americas in the first place, and could not have forgotten them. They barely knew there had been "people who left" much less where they had gone.