Photonic time crystals are artificial materials whose electromagnetic properties are uniform in space but periodically vary in time. The synthesis of these materials and experimental observation of their physics remain very challenging because of the stringent requirement for uniform modulation of material properties in volumetric samples. In this work, we extend the concept of photonic time crystals to two-dimensional artificial structures-metasurfaces. We demonstrate that time-varying metasurfaces not only preserve key physical properties of volumetric photonic time crystals despite their simpler topology but also host common momentum bandgaps shared by both surface and free-space electromagnetic waves. On the basis of a microwave metasurface design, we experimentally confirmed the exponential wave amplification inside a momentum bandgap and the possibility to probe bandgap physics by external (free-space) excitations. The proposed metasurface serves as a straightforward material platform for realizing emerging photonic space-time crystals and as a realistic system for the amplification of surface-wave signals in future wireless communications.