This study shows the land bridge was open from ~36 ka to ~11 ka which fits with our current, non controversial, understanding and timing for crossing Beringia and travelling south by coastal routes (the Ice Free Corridor didn't open until later). Scientists have traditionally agreed that the earliest dates that humans were found in North America is somewhere between 14,000 to 16,000 years ago, which is supported by recent findings, give or take:

The oldest stemmed points (pre-Clovis) in North America have been dated to ~16,000 cal yr B.P. and are in Cooper's Ferry Idaho. These findings are not controversial and have been widely accepted: Dating of a large tool assemblage at the Cooper’s Ferry site (Idaho, USA) to ~15,785 cal yr B.P. extends the age of stemmed points in the Americas

Other findings, such as the oldest foot prints, located in White Sands National Park in New Mexico, date back to between 23,000 and 21,000 years ago. However, these dates are highly controversial and several authors have called for improved methods to date them: A critical assessment of claims that human footprints in the Lake Otero basin, New Mexico date to the Last Glacial Maximum

The tiny seeds of an aquatic plant (Ruppia cirrhosa) were used to age the footprints last year are at the center of the timeframe debate. Ruppia cirrhosa, grows underwater and gets a lot of its carbon for photosynthesis from dissolved carbon atoms in water. It's possible that carbon in the water came from a much older reservoir than when the foot prints were made:

>"The dating of those footprints is crucial in interpretations of when humans first came to North America from Asia, but the ages have larger uncertainties than has been reported. Some of that uncertainty is related to the possibility of a radiocarbon reservoir in the water in which the dated propagules of Ruppia cirrhosa grew. As a test of that possibility, Ruppia specimens collected in 1947 from nearby Malpais Spring returned a radiocarbon age of ca. 7400 cal yr BP. We think it would be appropriate to devise and implement independent means for dating the footprints, thus lowering the uncertainty in the proposed age of the footprints and leading to a better understanding of when humans first arrived in the Americas."

Other sites such as those at Bluefish Caves (controversial) and Old Crow river basin (was controversial not sure if it still is) fit with the timing of the land bridge being exposed and flooded. While other foot prints found on Calvert Island along the coast of British Columbia date to 13,000 years old: Terminal Pleistocene epoch human footprints from the Pacific coast of Canada

What's rather surprising here is the rapid growth of the ice sheets, and the resulting drop in sea level, occurring surprisingly quickly and much later in the glacial cycle than previous studies had suggested.