More would have arrived if they came by a land bridge, IMHO.
The land bridge still seems to have been the source for most migration. There were one or more coastal migrations, but they seem to have been small, and didn't result in much spread to the interior.
Here is a good recent article: Beringian Standstill and Spread of Native American Founders.
There’s a later migration about 5,000 BC. We know them from their languages.