Monolayer semiconductors are emerging platforms for strong nonlinear light-matter interaction, which is enhanced by the giant oscillator strength of tightly bound excitons. Little attention has been paid to the impact of excitonic resonances on the temporal dynamics of nonlinear light-matter interaction, since harmonic generation and optical-wave mixing are generally considered instantaneous processes. We find that a significant time difference, ranging from -40 fs to +120 fs, is necessary between two light pulses for optimal sum-frequency generation (SFG) and four-wave mixing (FWM) to occur from monolayer WSe2 when one of the pulses is in resonance with an excitonic transition. These resonances involve both band-edge A-excitons (AX) as well as high-lying excitons (HX) comprising electrons from conduction bands far above the gap. Numerical simulations of the density-matrix evolution reproduce and explain the distinct dynamics of SFG and FWM. The interpulse delays for maximal SFG and FWM are governed primarily by the lifetime of the one-photon and two-photon resonant states, respectively. The method therefore offers an unconventional probe of excitonic dynamics that are either one-photon or two-photon allowed. Remarkably, the longest delay times occur at the lowest excitation powers, indicating a strong nonlinearity that offers exploration potential for excitonic quantum nonlinear optics.