While some languages, like Basque in Europe, are considered "language isolates," meaning they don't have any demonstrably close relatives, they still share features with other language families, indicating a common origin somewhere in the distant past.
It's possible that extinct languages could have been truly unrelated, but with no surviving speakers or records, it's impossible to know for certain.
The idea of a completely unrelated language is a fascinating concept, but the current state of linguistic knowledge suggests that all languages are ultimately connected through shared ancestry.