The scale of the Great Lakes implies very effective agents of erosion. Whatever the process, it must also have eroded the rock basins of other lakes around the perimeter of the Canadian Shield, including Great Bear, Great Slave, and Athabasca lakes, all hundreds of meters deep and cut into bedrock. There has been a long controversy about the question. But Lake Superior extends to well below sea level.
Rivers seem inadequate too.
The answer, of course, is catastrophic currents. Currents that formed the lake basins were fast, and sustained. This implies powerful uplifts of large areas of the earth's crust, that spilled enormous volumes of water over the area now occupied by the Great Lakes. Remnants of the former sediment cover remain as outliers in different parts of the Shield. Outliers occur at New Liskeard, Ontario, and scattered locations in Quebec.