  A strong first-order electroweak phase transition (EWPT) can be induced by
light new physics weakly coupled to the Higgs. This study focuses on a scenario
in which the first-order EWPT is driven by a light scalar $s$ with a mass
between 15-60 GeV. A search for exotic decays of the Higgs boson into a pair of
spin-zero particles, $h \to ss$, where the $s$-boson decays into $b$-quarks
promptly is presented. The search is performed in events where the Higgs boson
is produced in association with a $Z$ boson, giving rise to a signature of two
charged leptons (electrons or muons) and multiple jets from $b$-quark decays.
The analysis is considering a scenario of analysing 5000 fb$^{-1}$ $e^+ e^-$
collision data at $\sqrt{s} = 240 $ GeV from the Circular Electron Positron
Collider (CEPC). This study with $4b$ final state conclusively tests the
expected sensitivity of probing the light scalars in the CEPC experiment. The
sensitivity reach is significantly larger than that can be achieved at the LHC.
