While there's certainly a gap in the teaching of other cultures in most (all?) modern education, do note that (here from Wikipedia): "History (...) is the study of the past as it is described in written documents. Events occurring before written record are considered prehistory. It is an umbrella term that relates to past events as well as the memory, discovery, collection, organization, presentation, and interpretation of information about these events."
To the best of my knowledge, there's a limited written record from the North America prior to the invasion (" discovery") - apart from in Norse sagas chronicling the viking arrival around 1000 AD (and while the sagas are an important source, they're hardly known for their reliability, in part because of the often long gap between events and when the sagas were first written down).
Both south and north American indigenous civilizations were AFAIK largely without a written record.
That is a controversial definition that many academics criticize because of the ridiculous questions it raises. Most Archaeologists and anthropologists use broader definitions of history that encompass a whole host of non-literary sources precisely because it's stupid to discuss whether Americans became historic the second someone happened to write about them in 1492 or if linear-a tablets need to be translated before Minoans are considered historical.
To the best of my knowledge, there's a limited written record from the North America prior to the invasion (" discovery") - apart from in Norse sagas chronicling the viking arrival around 1000 AD (and while the sagas are an important source, they're hardly known for their reliability, in part because of the often long gap between events and when the sagas were first written down).
Both south and north American indigenous civilizations were AFAIK largely without a written record.