I don't think so. The theory is that the land bridge across the Bering Sea approximately 13,000 years ago was caused by declining sea levels due to glaciation on the continents.
This was the time when glaciers were carving Yosemite Valley, for example.
There might well have been some snow on the Bering Sea landbridge, but not a whole lot as snowfall has always been light in that area.
The problem is that the land bridge was definitely not there 40,000 years ago, so any migration to the Americas would have to have been by boat or raft, a difficult and dangerous proposition at best.
Somebody apparently made it, though, if the evidence from Mexico is credible.
However, since we haven't found much evidence, if any, of a human presence between the period of 13,000 years ago and this evidence of 40,000 years ago, it is suggestive that whoever made that earlier passage was unable to maintain a population.
Whoever made this footprint in the ash might well have ended up as supper for a saber-toothed cat.
It could also be that many of the areas of denser population in that time are now under water.
I still have problems when trying to understand the Bering Sea Bridge thing. I admit to no education in the subject area so it’s all pure guess on my part, but...
The Bering Sea loc vic where the bridge is supposed to have been is clogged with ice during winter now, and it’s not an ice age.
If the ice sheets were thick enough to cover the top half of the North American continent, then the ice cap at sea must have been equally large and extended. The ice cap on land at the other side of the bridge would be down past the bridge entrance as well.
This would seem to me to mean that any migrating critters and/or peoples would have had to climb up on the huge, barren, lifeless and wildly dangerous ice cap, travel all the way along that ice cap to where it crossed the sea, all the way across the sea, and all the way down the other side of the ice cap.
All that, instead of moving south away from the ice where there was such luxuries as food, shelter, unfrozen water, and at least some potential for survival.
Now, if the sea was 200m or so shallower due to all that ice, how much closer would the shores, and how much more prominent would the various islands along the way have appeared to be?