Percolative superconductivity frequently arises in two-dimensional van der Waals materials due to reduced dimensionality, enhanced quantum fluctuations, and complex electron-phonon interactions, providing a unique platform where normal electrons coexist with Cooper pairs. We report the observation of substantial third-order nonlinear transport in a trilayer 1T^′-MoTe₂ superconductor within its percolative transition regime. The third-harmonic longitudinal voltage (V_|^(3ω)) exhibits a clear cubic dependence on excitation current below a threshold, with both its magnitude and nonlinear coefficient strongly correlated with the superconducting state. This nonlinear response is semiquantitatively captured by the superconducting fluctuation within the time-dependent Ginzburg-Landau theory, where nonlinear transport arises due to fluctuating Cooper pairs. Our results demonstrate that third-order nonlinear transport serves as a sensitive probe of superconducting transitions in percolative systems and establish a foundation for exploring higher-order transport phenomena in strongly correlated systems.