  The electroweak phase transition can be made first order by extending the
Standard Model (SM) Higgs sector with extra scalars. The same new physics can
explain the matter-antimatter asymmetry of the universe by supplying an extra
source of CP violation and sphaleron processes. In this paper we study the
existence of a strong first order electroweak phase transition (SFOEWPT) in the
type-I and type-II two Higgs doublet models (2HDM). We focus on how the SFOEWPT
requirement constraints the spectrum of non-SM Higgs. Through a parameter space
scan, we find that SFOEWPT suggests upper limits on the masses of heavy Higgs
$m_{A/H/H^\pm}$, which is less than 1 TeV. High temperature expansion and Higgs
vacuum uplifting is used for an analytical understanding of our results. We
also study the probe ability on SFOEWPT from Higgs and $Z$-pole precision
measurements at the one-loop level at future Higgs & $Z$ factories. And
together with theoretical constraints, sizeable loop corrections require $m_A
\approx m_{H^\pm} > m_H$ to meet SFOEWPT condition in Type-II 2HDM.
