What is "since before" without anything between these two words?

If it was just “... before the coming of whites” without the “since,” it would suggest that their occupation stopped when the white people came.

The “since” is necessary to indicate that the period of occupancy spanned the period from before the coming of the white people to after thymes arrived to today.

If we consider that the coming of whites took place at a certain point in time, "since before the coming of whites" works well to refer to some period starting at some indefinite point before and continuing up to the coming of whites.

For example, if the coming of whites refers to the discovery of America by Columbus in 1492, "since before the coming of whites" could refer to a period of time extending from some previous time (say, in 15,000 BC) up to 1492.

For further reference, we can see this Wikipedia article as well as this related one, which refers to the arrival of the first aborigines in America.

My claim is that "since before X" works well when one knows the end but ignores the beginning of the period in question.