  The significance of the electroweak phase transition is undeniable, and
although initially it was believed that it was second-order, it is now believed
that it is a first-order transition. However, it is not a strong first-order
phase transition in the context of the Standard Model and the remedy to this
issue is to use the Higgs portal and directly couple the Higgs to a hidden
scalar sector. This can result in a strong electroweak phase transition, while
the couplings to a hidden scalar are constrained by several phenomenological
constraints, such as the sphaleron rate criterion and the branching ratio of
the Higgs to invisible channels. In this work, we consider the standard singlet
extensions of the Standard Model, including dimension-six non-renormalizable
operators that couple a real singlet scalar field with the Higgs doublet. As a
result, we examine the effects of those Higgs-singlet couplings on the
electroweak phase transition. The effective theory, where the
non-renormalizable couplings originate from, is considered to be active beyond
15$\,$TeV. As we show, the Universe experiences a two-step electroweak phase
transition, a primary phase transition in the singlet sector at a high
temperature, and then a subsequent first-order phase transition from the
singlet vacuum to the electroweak vacuum. The singlet's phase transition can
either be second-order or first-order, depending on the singlet mass and its
couplings to the Higgs. In particular, we show that the dimension-six operator
assists in generating a strong electroweak phase transition in regions of the
parameter space that were excluded in the previous singlet extensions of the
Standard Model. This is further apparent for low singlet masses \(m_S < m_H/2\)
which are rarely taken into account in the literature due to the invisible
branching ratio of the Higgs boson.
