In the presence of a real singlet scalar field with Z 2 symmetry in addition to the Higgs field in the Standard Model, we analytically investigate all possible one-step and two-step electroweak phase transitions (EWPT) in the high-temperature expansion limit. In particular, we examine the possibility of a first-order phase transition in an intermediate temperature interval of the universe for two- step scenarios. In all scenarios, we provide with necessary conditions on the parameters of the model to address a first- or second-order phase transition if ever possible in the high-temperature approximation. We show that among all possible EWPT channels in this model, only the two-step phase transition (0 , 0) → (0 , w ) → ( v, 0) can be of first-order type, either in the first or second step. The conditions obtained for EWPT is confronted with the dark matter (DM) and collider constraints. It is shown that the second-order one-step (0 , 0) → ( v, 0) scenario can evade the DM constraints, but it is not accessible to future colliders. The two-step first-order EWPT scenario (0 , 0) → (0 , w ) → ( v, 0), except for small DM masses, is excluded by direct detection experiments XENON1T/LUX, but it is accessible in future colliders ILC/TLEP.

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