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In high-Tc cuprates and alkali doped fullerides, driving of specific phonon modes with mid-infrared laser pulses has been shown to induce transient superconducting-like optical properties for temperatures far above the equilibrium Tc. Here, we discuss an analogous effect in the quasi two-dimensional organic superconductor κ-(ET)₂Cu[N(CN)₂]Br. At equilibrium, this material bears similarities to high-Tc cuprates, showing unconventional superconductivity that emerges from a correlated metallic state with a Tc of 11 K. In a series of non-equilibrium experiments, we resonantly excite local vibrational modes of the ET molecule and probe the transient conductivity of the material with THz spectroscopy. Starting from the equilibrium metallic state at T >> T_C, we observe a photo-induced response compatible with that of a transient superconductor, which is strongly reduced when the pump wavelength is tuned away from vibrational resonances. When performing the experiment across the bandwidth tuned phase diagram of this family of compounds, this effect is observed only in κ-(ET)₂Cu[N(CN)₂]Br, indicating that proximity to the Mott insulating phase and possibly the presence of preexisting superconducting fluctuations are prerequisites for this effect.