Strongly correlated quantum matter, such as interacting electron systems or interacting quantum fluids, exhibits properties that defy explanation in terms of linear fluctuations and free quasiparticles. In these systems, quantum fluctuations are large and generically display non-Gaussian statistics—a property captured only by inspecting high-order correlations, whose quantitative reconstruction presents a challenge for both experiments and theory. A prime example of correlated quantum matter is the strongly interacting Bose fluid, realized first in superfluid helium and, more recently, in ultracold atoms. Here, we experimentally study interacting Bose gases from the weakly to the strongly interacting regime through single-atom-resolved correlations in momentum space. We find that the Bogoliubov pairing among modes of opposite momenta, characteristic of the weakly interacting regime, is suppressed as interactions grow. This departure from the predictions of Bogoliubov theory marks the onset of the strongly correlated regime, as confirmed by numerical simulations that highlight the role of nonlinear quantum fluctuations in our system. Furthermore, our measurements reveal a non-zero four-operator cumulant at even stronger interactions, which is a direct signature of non-Gaussian correlations. These results shed light on the emergence and physical origin of non-Gaussian correlations in ensembles of interacting bosons.