I think the Baring sea can freeze over midwinter allowing crossing.
With regard to the 'last ice age' according to my local football team head coach who has a degree in Geology, we are still in ice age due to having polar ice caps.
It would be interesting to have that map overlaid with a topological map (if that is the right term) and other information to reflect what the earth looked like back then. Of course it probably took them a long long time to even migrate, given going from I guess sub saharan Africa to modern Day Canada / USA on foot would take a long time.