We study the occurrence of a strong first-order electroweak phase transition in composite Higgs models. Minimal constructions realising this scenario are based on the coset SO(6)/SO(5) which delivers an extended Higgs sector with an additional scalar. In such models, a two-step phase transition can be obtained with the scalar singlet acquiring a vacuum expectation value at intermediate temperatures. A bonus of the Nambu-Goldstone boson nature of the scalar-sector dynamics is the presence of non-renormalisable Higgs interactions that can trigger additional sources of CP violation needed to realise baryogenesis at the electroweak scale. Another interesting aspect of this scenario is the generation of gravitational wave signatures that can be observed at future space-based interferometers.New physics models in which the Higgs boson arises as a pseudo Nambu-Goldstone Boson (NGB) from a strongly interacting theory can provide other natural scenarios in which first-order transitions can be obtained. The simplest models realising the idea of a NGB Higgs, the minimal Composite Higgs Models (CHMs) [21], are based on the symmetry breaking pattern SO(5) → SO(4), which delivers the four real scalar degrees of freedom that build-up a SM-like SU(2) Higgs doublet. In these scenarios the Higgs couplings are modified, but the strong experimental constraints already put an upper bound of order 10% on these deviations [22,23]. Moreover direct and indirect searches exclude additional composite resonances for masses below ∼ 1 TeV [24][25][26]. For these reasons the corrections to the Higgs thermal potential are necessarily small and can not convert the EWPhT into a strong first-order one.Successful CHMs exhibiting a first order EW transition can instead be realised by considering non-minimal symmetry-breaking patterns. A simple possibility, on which we will focus in this work, is provided by the coset SO(6)/SO(5) [27,28], in which the Higgs doublet is accompanied by an extra real scalar η. In this case the effective potential for the scalar fields allows for a much richer phase-transition behaviour. The EW transition may proceed directly from the symmetric phase to the EW-symmetry-breaking (EWSB) one or via some intermediate steps. The latter possibility is particularly interesting. As we will see, in a large part of the parameter space of the model, a two-step EWSB transition can be realised, in which the singlet gets a vacuum expectation value (VEV) at intermediate temperatures. In such case, the presence of a H 2 η 2 portal interaction creates a barrier between the EW vacuum and the intermediate vacuum, giving rise to a first-order transition that can be strong enough to allow for baryogenesis.Another interesting aspect of the composite scenario is the fact that the NGB nature of the Higgs implies the presence of non-renormalisable Higgs interactions that can provide additional sources of CP violation. As we will see, interactions of the form η ht L t R , are naturally there in SO(6)/SO(5) models and can trigger CP-violating effec...