Mathematically / statistically "safe" way to differentiate between crypto and random blob?
If anything can distinguish a blob of random data from an encryption of some (known) data (other than any intentionally added data formats, like a header or a length difference), the encryption algorithm is called broken.
(This is one of the variants of the ciphertext  indistinguishability criterion for ciphers.)

As there are several encryption algorithms which seem to fulfill this criterion, this means in reverse, no, you can't prove that some self-created blob of random data is really random.

A possible solution would be to have some third party generate the random data for you, and sign a confirmation that it is random. I'm not sure that there is such a service – while random.org offers random numbers (or bytes), I don't see something which can certify those.
(One idea would be to store a transcript of the TLS connection by which you downloaded it, but that can also be faked.)

You can download pregenerated files from random.org – assuming random.org isn't part of your conspiracy, this should be good enough to prove you don't have encrypted data there. (But it would also be utterly useless to carry them around in your USB drive, other than to annoy the border guards.)

Another thing to keep in mind: Even if you have real random data with you (which you might previously have shared with someone else), you (or your partner) can later use this to encrypt plaintext (using a one-time-pad) to be sent over the Internet. So allowing you to bring random data into the country just opens the way for you to use encryption later.