The “Bering Strait” thing never made much sense to me... To say that man followed the Mammoth across the ice sheet is alright, but what exactly were the Mammoths eating for a thousand mile trek over ice? It is far more palatable to assume man followed the edge of the ice (or island hopping) in boats, fishing and hunting seals to arrive by the Bering Sea... And if boats, there is no longer a need to assume a northern passage at all.
Bering always seemed suspect to me. The cultures get more sophisticated the further away you are from the straits.
I’d suspect landings further south with the northern primitives as refugees from failed societies.