Third harmonic generation (THG) microscopy offers label-free imaging and enables three-dimensional imaging with inherently good optical depth-sectioning. Its utility is important for imaging and characterization of laser-induced changes in transparent materials. Here we develop a digital twin for THG microscopy that allows accurate simulation of experiments and provides insight into desired information such as the third-order nonlinear susceptibility tensor. It also enables accurate simulation of the instrument's point spread function (PSF), which is essential for relating THG measurements to the desired hidden quantities. Finally, we improve microscope throughput with adaptive optics, demonstrating how PSF engineering improves spatial probing, temporal efficiency, and information content, and comparing results between the real setup and its digital twin.