  Interactions between light and matter allow the realization of
out-of-equilibrium states in quantum solids. In particular, nonlinear phononics
is one of the efficient approaches to realizing the stationary electronic state
in non-equilibrium. Herein, by using extended $ab~initio$ molecular dynamics,
we identify that long-lived light-driven quasi-stationary geometry could
stabilize the topological nature in the material family of HgTe compounds. We
show that coherent excitation of the infrared-active phonon mode results in a
distortion of the atomic geometry with a lifetime of several picoseconds. We
show that four Weyl points are located exactly at the Fermi level in this
non-equilibrium geometry, making it an ideal long-lived metastable Weyl
semimetal. We propose that such a metastable topological phase can be
identified by photoelectron spectroscopy of the Fermi arc surface states or
ultrafast pump-probe transport measurements of the nonlinear Hall effect.
