  We report on an ultrafast photoinduced phase transition with a strikingly
long-lived Martensitic anomaly driven by above-threshold single-cycle terahertz
(THz) pulses in Nb$_3$Sn. A non-thermal, THz-induced depletion of low frequency
conductivity indicates increased gap splitting of high energy $\Gamma_{12}$
bands by removal of their degeneracies which enhances the Martensitic phase. In
contrast, optical pumping leads to a $\Gamma_{12}$ gap melting. Such
light-induced non-equilibrium Martensitic instability persists up to a critical
temperature $\sim$100 K, i.e., more than twice the equilibrium temperature, and
can be stabilized beyond technologically-relevant, nanosecond timescales.
Together with first-principle simulations, we identify a compelling THz tuning
of structural fluctuations via E$_u$ phonons to achieve a non-equilibrium
ordering at high temperatures far exceeding those for equilibrium states.
