  We develop a non-perturbative approach for calculating the superconducting
transition temperatures ($T_{c}$) of liquids. The electron-electron scattering
amplitude induced by electron-phonon coupling (EPC), from which the effective
pairing interaction can be inferred, is related to the fluctuation of the
$T$-matrix of electron scattering induced by ions. By applying the relation,
EPC parameters can be extracted from a path-integral molecular dynamics
simulation. For determining $T_{c}$, the linearized Eliashberg equations are
re-established in the non-perturbative context. We apply the approach to
estimate $T_{c}$ of metallic hydrogen liquids. It indicates that metallic
hydrogen liquids in the pressure regime from $0.5$ to $1.5\mathrm{\,TPa}$ have
$T_{c}$ well above their melting temperatures, therefore are superconducting
liquids.
