Always. However, I do not believe the Bering land bridge was the primary means of access to America. Why trudge through endless miles of muskeg when you can paddle along at a much faster pace with a lot more provisions in a boat. If the aborigines, relatives of those in Australia, arrived 50,000 years ago, they would leave little sign of an archaeological nature. There is not enough data for more than a tentative timeline, although we are finally starting to dig in America and letting somebody else dig in Egypt, Babylon, and elsewhere, and should be ready for some assumption-exploding discoveries.
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