From a Wikipedia article about Beringia:
A reconstruction of the sea-level history of the region indicated that a seaway existed from c. 135,000 – c. 70,000 YBP, a land bridge from c. 70,000 – c. 60,000 YBP, an intermittent connection from c. 60,000 – c. 30,000 YBP, a land bridge from c. 30,000 – c. 11,000 YBP, followed by a Holocene sea-level rise that reopened the strait. Post-glacial rebound has continued to raise some sections of the coast.
So 130,000 years ago, if that's assumed precise, it'd been here a while if it came over land, not across water.
One possibility is they are simply wrong about how early H. sapiens left Africa. The remaining evidence does not have to tell the full story, much may have been lost .. much HAS been lost, we just don't know which parts.