It doesn't even need to be random. What if you send an instance of a proprietary file format? Is the company required to share the spec and toolchain so that the govt can verify it (probably) isn't an encrypted message?
Exactly - or encrypted payloads hiding inside standard image file formats. Basically steganography. If all you want to send is a small encrypted text message, it should be possible to hide that in a large image (encoding in the LSB or whatever) in just a small percentage of pixels so that it doesn't fail statistical tests and is indistinguishable from real noise.
In my home directory is a 4GB random file. I suggest you should do this too. Vary the filename to taste. Some suggestions: the name of any active drug market or cyber threat actor.
I came about a Google subscription which includes 2TB of storage. I filled it with crypto noise (ok, Gemini did it for me). I couldn't let it be unused. Will have to delete it when the subscriptions runs out.