Is there any sort of encryption scheme that would make it possible to generate a key on-demand to decrypt only the data that was encrypted within some arbitrary

Is there any sort of encryption scheme that would make it possible to generate a key on-demand to decrypt only the data that was encrypted within some arbitrary interval of time? The idea being if 100 terabytes of someone's private life history is seized, a judge could order the decryption of only the parts likely to contain material evidence. The closest thing that comes to mind is to use a unique AES key for every chunk of 5 minutes or so, and then encrypt those keys with an asymmetric cipher with the private key secured off-site somewhere, which could selectively decrypt some of the AES keys. But that could be an inconveniently long list of keys for, say, 10 video feeds over several days.