Efficient sensors for terahertz (THz) frequency range are in high demand for applications in biomedicine, chemistry, security, and electronics. Conventional thin-film sensing relies on spectroscopy, while improved sensitivity can be achieved using frequency selective electromagnetic metasurfaces (FSMSs). A simpler and innovative approach involves a nonspectroscopic method using a single-frequency THz source and an angle-dependent metasurface (MS) under oblique illumination. This method derives analyte parameters from the shift in the resonant transmission angle. We further develop this platform and investigate a new MS operating at 0.139 THz, exhibiting a strong variation of a narrow stopband with the angle of incidence. Theoretical, numerical, and experimental results demonstrate the MSs ability to detect submicrometer-thick films. The proposed nonspectroscopic sensing technique offers a promising avenue for highly efficient and sensitive detection of dielectric thin films.