Alternative methods for observing Grand Unification?

[Ghostcrown]

Do we have any alternative routes to explore besides constructing a particle accelerator that reaches energies on the scale of ~10¹⁶ GeV to observe the unification of the electroweak and strong forces? And if not, does that mean we're left with nothing but speculation and mathematics?

 

[mfb]

Precision measurements might help: even if we cannot create particles with that energy in accelerators directly, they can contribute to processes as virtual particles. That's how three of six quarks were predicted and how the Higgs mass had a reasonable estimate even before it was discovered.
An observation of proton decay would be a very interesting test, as some GUT models predict it.

Those theories could also lead to some relationship between things we have as independent free parameters in the standard model - parameters we can measure at low energy.