The premise contains two errors:
The Great Lakes are remnants of glacial Lake Algonquin, Lake Chippewa, Lake Nipissing—proglacial lakes that filled the basin as the Laurentide Ice Sheet retreated (~14,000–8,000 years ago). Those ancestral lakes were larger because:
As ice retreated, outlets lowered (Niagara, St. Lawrence), crust rebounded (isostatic uplift, still ongoing ~30 cm/century at Hudson Bay), and climate warmed. Modern lakes stabilized ~3,000 years ago at current levels.
Lake Agassiz (Manitoba/NW Ontario/MN/ND) was the true giant—440,000 km², larger than the Caspian. It drained catastrophically (~8,200 ya), possibly triggering the 8.2 ka cooling event.