Do gluon jets occur spontaneously in the real world, or only in a particle accelerator?

Extremely high-energy cosmic rays, when they strike the Earth's atmosphere, spontaneously cause many of the reactions that we normally see only in particle accelerators, and in particularly high-energy cases it would not at all be surprising to see a gluon jet. In fact, their energy is often orders of magnitude higher than we can produce in particle accelerators. The highest-energy cosmic ray possessed something like 320 EeV, or equivalently 320 million TeV, of energy, while the LHC produces collisions with a center-of-mass energy of a measly 13 TeV in comparison.

As far as actually directly observing a gluon jet from a cosmic-ray interaction in the upper atmosphere, the main problem is that we don't really have too many particle detectors that are just sitting in the upper atmosphere, at a spot where a high-energy cosmic-ray interaction happens to take place. So we inevitably observe these reactions from a significant distance, which means the short-length characteristics of the reaction are often obscured by the resulting particle shower as the products of the reaction hit other particles in the atmosphere, dispersing their energy over a wider and wider cone.