Efimov physics is a leading research theme in recent few-body quantum physics. It also provides a very stimulating playground to explore novel forms of quantum matter. However, not much is known about its relevance in a many-body context. Here, we address this question in a mass-and-density imbalanced two-species fermionic mixture with a positive scattering length. We identify a range of mass ratios and densities for which the system undergoes a phase transition to a gas of universal trimers closely related to Efimov physics. We study the trimer-trimer interaction and find it to be repulsive at low energy. This suggests that the trimer phase is a stable SU\((3)\) Fermi liquid. The stability against recombination losses makes it specially appealing for cold-atom experiments. A fermionic \(^6\)Li-\(^{53}\)Cr mixture is a leading candidate to observe experimentally this trimer phase. These results are a first step towards the exploration of novel many-body ground states whose building blocks are universal clusters connected to Efimov physics.