We present an exploratory study that suggests that Efimov physics, a leading research theme in few-body quantum physics, can also induce stable many-body ground states whose building blocks are universal clusters. We identify a range of parameters in a mass-and-density imbalanced two-species fermionic mixture for which the ground state is a gas of Efimov-related universal trimers. An explicit calculation of the trimer-trimer interaction reveals that the trimer phase is an SU$(3)$ Fermi liquid stable against recombination losses. We propose to experimentally observe this phase in a fermionic $6$Li-$\mathrm{<mrow\; data-mjx-texclass="ORD">53</mrow>}$Cr mixture.