Crossing the country without a compass? First, I'm betting that it was done on foot before "discovery" by Columbus. It is known that a member of the Nez Perce tribe traveled to Cincinnati Ohio then home via Arizona and California. (No written record, but legends of this journey have been passed down by both the Nez Perce, the Cincinnati tribe and other tribes along the route.)
This planet has been circumnavigated without a compass or any other instruments. By an American, Professor Marvin Creamer, 1982. No timepiece, no sextant, no radio. A modern sailing yacht but all navigation was done with tools available before the written word. (Stars, sun, sky, weather, water colors and waves, birds, fish and animals, smells ...)