If we know the geographical origin of Native Americans, wouldn't it be logical for all of them to belong to a single language family?

The short version: If Native American languages do represent a single family, the connections are too obscured by time for linguistics to recognize.

The long version: A language family is only as large as a linguist's ability to make reliable connections between languages, and to distinguish those connections from a sprachbund (a group of languages that share similarities due to geographic proximity rather than a common ancestor). The farther you go into the past in attempting to reconstruct (pre-)historic languages, the more those connections get obscured. This is why the vast majority of major language families have roots that go back only to about 5,000 years ago, plus or minus a thousand. Beyond that point, linguists are working with theoretical reconstructions which are fare less reliable than dealing with the real thing.

The peopling of the Americas happened at least 16,000 years ago, probably closer to 20,000 years ago. You can add another 5,000 years or so if you start counting from the time when the ancestors of the earliest Americans became more or less genetically isolated from the rest of Eurasia - at which, point we don't know if that population would have represented a single language family or multiple languages spoken by people interacting in an isolate area. Remember, genetics and linguistics aren't linked. Even if that population spoke a single language, that's plenty of time for multiple language families to develop.

That said, there have been some attempts to discover a theoretical Amerind Language Family, which would represent most of the Americas excluding the far north. This was proposed by Joseph Greenberg back in the 1960s, but hasn't been accepted by most linguists. The Amerind language family relies on several hypothetical macro-families being accurate, such as the proposed links between Algonquian languages and Salish languages, Siouan languages and Iroquoian languages, Muskogean languages and Natchezean languages, etc. The connections within these macro-families are tenuous at best. In some cases, like the Muskogean / Natchezean connections, they may more accurately represent a sprachbund than a language family. The major problem with the Amerind Language Family gets back to my original point. Proto-Amerind would have been spoken so long ago and its descendant languages changed so much without leaving a linguistic fossil record in the form of written languages, that the proposed connections have essentially been reduced to a handful of generalities that aren't even universal within the proposed languages. The "n / m" trend in first and second person pronouns being the most famous and was noticed well before Greenberg. But it's not found in all "Amerind Languages." For example, in Chickasaw, "I" is ana'akot. One point in favor of Amerind. But "You" is ishnaakot. No luck there. In the case of Iroquoian languages other than Cherokee, they don't even have the m sound. The first person singular agentive affix and the second person singular agentive affix (the closest parallels to I and you) are ke- and se-, respectively, in Oneida, for example. That doesn't fit with the Amerind theory at all.