Second-order optical effects are essential to the active control of light and the generation of new spectral components. The inversion symmetry, however, prevents achieving a bulk χ^{(2)} response, limiting the portfolio of the second-order nonlinear materials. Here, we demonstrate subpicosecond conversion of a statically passive dielectric to a transient second-order nonlinear medium upon the ultrafast transfer of hot electrons. Induced by an optical switching signal, the amorphous dielectric with vanishing intrinsic χ^{(2)} develops dynamically tunable second-order nonlinear responses. By taking the second-harmonic generation as an example, we show that breaking the inversion symmetry through hot-electron dynamics can be leveraged to address the critical need for all-optical control of second-order nonlinearities in nanophotonics. Our approach can be generically adopted in a variety of material and device platforms, offering a new class of complex nonlinear media with promising potentials for all-optical information processing.