You'll not be able to prove validity of the concepts behind this school of therapy themselves in any other sense, even if you would be able to identify some coherent set of concepts from all the various techniques and approaches that CBT subsumed over the years.
And certainly just because "if you follow these practices, you will maybe get better" metric does not say anything about validity of the concepts of a particular school of therapy in any case, no matter what school you're talking about.
I mean yeah, many people usually care about whether some therapy works and how well, and not whether the concepts that you're told in therapy to justify what the therapy is doing make coherent sense or can be scientifically validated, so this is usually not a problem for people in need of care. But idea that CBT's concepts are more objective than other mumbo jumbo therapies out there is just plain wrong.