It wasn't a one day, hey there is this little thin chunk of land spaning 50 miles, lets walk across. It was a very large piece of land that connected the continents and could have been slowly expanded over over thousands of years.... there was no route to paddle that was shorter than walking.... it extended half way across canadas northern border and from siberia all the way to china on the asian side.... the idea it was this little sliver and only 50 miles wide is not a correct assumption.
There was no, hey I stand on this shore I see the other shore, it was one large piece of land.. in fact if one was to sail from asia to the americas the trip would have been largely the same as it is today once you were far enough south to have ocean. Take a look at some photos here