The energy of an electromagnetic wave is converted as the wave passes through a temporal boundary. Thus, effective temporal control of the medium is critical for frequency conversion. Here, we propose rapidly time-variant metasurfaces as a frequency-converting platform and experimentally demonstrate their efficacy at terahertz frequencies. The proposed metasurface is designed for the sudden merging of two distinct metallic meta-atoms into a single one upon ultrafast optical excitation. This sudden merging creates a spectrally designed temporal boundary on the metasurface, by which the frequency conversion can be achieved and engineered. Interestingly, the time delay between the abrupt temporal boundary and the input terahertz pulse is found to be strongly related to the phase of the converted wave as well as its amplitude. As the proposed scheme does not rely on the nonlinearity, it may be particularly advantageous for the frequency conversion of waves with weak intensities.