  Recent experiments and calculations in topological semimetals have observed
anomalously strong second-order optical nonlinearity, but yet whether the
enhancement also occurs at surfaces of topological semimetals in general
remains an open question. In this work, we tackle this problem by measuring
polarization-dependent and rotational-anisotropy optical second harmonic
generation (SHG) from centrosymmetric type-II Dirac semimetal PdTe$_2$. We
found the SHG to follow C$_{3v}$ surface symmetry with a time-varying intensity
dictated by the oxidation kinetics of the material after its surface cleavage,
indicating the surface origin of SHG. Quantitative characterization of the
surface nonlinear susceptibility indicates a large out-of-plane response of
PdTe$_2$ with $|\chi_{ccc}^{(2)}|$ up to 25 $\times$ 10$^{-18}$ m$^2$/V. Our
results support the topological surfaces/interfaces as a new route toward
applications of nonlinear optical effects with released symmetry constraints,
and demonstrate SHG as a viable means to in situ study of kinetics of
topological surfaces.
