There were dozens of language families, each the equivalent of the Indo-European family, before 1492. This map is a “simplified” one. In today’s California, for instance, languages that are spoken by neighboring tribes are as different as French and Chinese.
Why did the Americas develop such linguistic diversity? Many linguists suspect that at least some of these separate families date back to separate migrations of different tribes from Asia who originally spoke unrelated languages. Linguistic and archaeological data hint at more than one migration from Asia into the Americas, all of them through Alaska.
Extra Fun Fact: see “Eskimo-Aleut” in northern North America? It is not colored because there is no evidence those languages are related to any other indigenous American languages!