Though it's not good for cryptographic security, you can probably script up something that runs an arbitrarily wide Linear Congruent Generator to push out bits/blocks of bits with long enough periodicity to get you the GB-worth of 'randomness' from anywhere within a potential TB/PB/more of its whole cycle (depending on seed). The mathematics of this is fairly well known (what to choose as a modulus, etc).
Or use a Linear-Feedback Shift Register like the XORShift method (easier to make the elemental binary work[1] without worrying about double-double-wide bitfields needing large relative-primes to be used in the mathematics). Just check the details on periodicity and make the state-width wide enough to add enough orders of magnitude above this to be happy. Then pump each byte (as you get it, whether as a trickle or a flow) into your ~GB reference file until it's large enough. First try it on a MB (if not KB) output, with the GB-capable algorithm, just to make sure you're not gonna wait five months. Shouldn't do (and if streaming to disc, the state-memory shouldn't strain your RAM capacity) but depends on how clunkily you implemented it.
Ummm...
TL;DR;, look up LCG and LFSR pseudocode, and any notes on best use, and see if either tickle your fancy.
[1] I could probably hack up a
very inefficient .BAT-based implementation, for at least the bitwise shuffling, but .sh, Java/Python/Perl and then actual compiled from a C-dialect/whatever would almost certainly be better with proper write-as-binary 'garbage-makers'. And if you're planning on sometbing like using the stream to flip raw pixel values, for codex-conversion/deconversion, you might be able to preformat it into the reference raw format of your choice and cut out the intermediate stage.