Oh, there was a land bridge. Several in fact, spread over tens of thousands of years. But most of the early migration came as it did throughout the rest of the Pacific Rim. By people in small coastal boats following the land. Just as those that reached places like Japan, Philippines, Indonesia, and Australia.
But we also know there was a land bridge simply by looking at what crossed. Interesting fact, the Equine prior to the land bridge was a North American only animal. All of those horses from Asia to Africa and Europe? All from descendants that crossed on the land bridge prior to the species becoming extinct in North America. So even ignoring any kind of pseudo-science nonsensical claims, the fact that horses went from North America to Asia is proof that humans could also do the same in reverse.
And I am one that believes that there was no "single colonization" of the Americas, but hundreds of them. Almost all differing groups, from dozens of years to hundreds of years apart. And other than a few exceptions, remaining along the seacoasts as that was how most of them lived. And it also explains many of the curious things found in the groups that did settle North America.
For those in the NW and Pacific Coast, fishing remained their main source of food until the modern era. Deer were hunted more for leather and to keep them from their plants than from an actual need to hunt them for food. And they all largely settled down into set areas, with very little migration. A huge difference from the nomadic Great Plains tribes, who seasonally followed large game and lived off of that. And this is in keeping with groups that would have started as coastal seafarers and lived at the edge of the coasts or on major rivers.
Me, I look at the tribes through the nation, and there are some rather huge differences between them. I do accept the Solutrean theory, that at least some did indeed migrate from Europe. But never any large amounts, just enough that those that came from Asia were able to learn their own unique stoneworking tricks and the "Clovis Point" was passed along before they genetically vanished in the "Indian Genetic Soup". Which is why the Clovis Point is very much like European stone tools of the era, but vastly different than those from Asia of the time. However, ultimately those few that came from Europe were genetically like drops of ink put into a bucket of milk, and diluted away. But there are some interesting genetic markers left in many tribes.
But even the claim that living in similar conditions will always result in similar behavior does not match, as the tribes of the US-Canadian NE did not live like their brethren in the NW. More agricultural, and also more dependent upon hunting as opposed to fishing. Common among either groups that had crossed the Continent so had adopted hunting to replace fishing, or those from Europe which in prehistory had more of a hunting tradition as they still had some incredibly massive creatures to contend with (Mastodons, woolly rhino, and the auroch just to start).
But one thing I have learned long ago, is to be highly suspicious of anybody that claims there is only "One Solution", and that anything other than their very strict linear one is correct. Me, you might say I see the human colonization of the Americas as a bunch of spaghetti. There was no one migration, but thousands of them. In many different ways. But that the final evidence left behind by those first inhabitants is forever out of reach, as they were a costal people. And until we enter another Ice Age, their first settlements and all the proof is now a dozen miles and more out to sea.
The above image may seem puzzling without context, but realize this was what the coastline was like at roughly 30-20,000 years ago. And that all the brown seen was back then dry land.
Then realize you are looking at the San Francisco Bay, around 18,000 years ago.