  Continuous and quantized transports are profoundly different. The latter is
determined by the global rather than local properties of a system, it exhibits
unique topological features, and its ubiquitous nature causes its occurrence in
many areas of science. Here we report the first observation of
fully-two-dimensional Thouless pumping of light by bulk modes in a
purpose-designed tilted moir\'e lattices imprinted in a photorefractive
crystal. Pumping in such unconfined system occurs due to the longitudinal
adiabatic and periodic modulation of the refractive index. The topological
nature of this phenomenon manifests itself in the magnitude and direction of
shift of the beam center-of-mass averaged over one pumping cycle. \rev{Our
experimental results are supported by systematic numerical simulations in the
frames of the continuous Schr\"{o}dinger equation governing propagation of
probe light beam in optically-induced photorefractive moir\'e lattice.} Our
system affords a powerful platform for the exploration of topological pumping
in tunable commensurate and incommensurate geometries.
