Ultrafast techniques have emerged as promising methods to study and control quantum materials. To maintain the quantum nature of the systems under study, excess heating must be avoided. In this paper, we demonstrate a method that employs the nonequilibrium laser excitation of planar-stretching optical phonons in tetragonal systems to quench an electronic nematic state across a quantum phase transition. Appropriately tuned off-resonant pulses can perform a quantum quench of the system either into the nematic phase (red detuning) or out of it (blue detuning). The nonlinear coupling of this phonon mode to nematicity not only mediates interactions in the nematic channel, but it also suppresses heating effects. We illustrate the applicability of our general results by considering the microscopic parameters of the nematic unconventional superconductor FeSe.