[en] A minimal extension of the Standard Model that provides both a dark matter candidate and a strong first-order electroweak phase transition (EWPT) consists of two additional Lorentz and gauge singlets. In this paper we work out a composite Higgs version of this scenario, based on the coset SO(7)/SO(6). We show that by embedding the elementary fermions in appropriate representations of SO(7), all dominant interactions are described by only three free effective parameters. Within the model dependencies of the embedding, the theory predicts one of the singlets to be stable and responsible for the observed dark matter abundance. At the same time, the second singlet introduces new CP-violation phases and triggers a strong first-order EWPT, making electroweak baryogenesis feasible. It turns out that this scenario does not conflict with current observations and it is promising for solving the dark matter and baryon asymmetry puzzles. The tight predictions of the model will be accessible at the forthcoming dark matter direct detection and gravitational wave experiments.