Maybe not impossible? https://en.wikipedia.org/wiki/Glueball#Mass_and_parity

Glueballs are predicted by quantum chromodynamics to be massive, despite the fact that gluons themselves have zero rest mass in the Standard Model.

These masses are on the same order of magnitude as the masses of many experimentally observed mesons and baryons, as well as to the masses of the tau lepton, charm quark, bottom quark, some hydrogen isotopes, and some helium isotopes.