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Context.Previous observations of the isolated Class 0 source B335 have presented evidence of ongoing infall in various molecular lines, such as HCO⁺, HCN, and CO. There have been no confirmed observations of a rotationally supported disk on scales greater than ~12 au. Aims.The presence of an outflow in B335 suggests that a disk is also expected to be present or undergoing formation. To constrain the earliest stages of protostellar evolution and disk formation, we aim to map the region where gas falls inwards and observationally constrain its kinematics. Furthermore, we aim to put strong limits on the size and orientation of any disk-like structure in B335. Methods.We used high angular resolution¹³CO data from the Atacama Large Millimeter/submillimeter Array (ALMA) and combined it with shorter-baseline archival data to produce a high-fidelity image of the infall in B335. We also revisited the imaging of high-angular resolution Band 6 continuum data to study the dust distribution in the immediate vicinity of B335. Results.Continuum emission shows an elliptical structure (10 by 7 au) with a position angle 5 degrees east of north, consistent with the expectation for a forming disk in B335. A map of the infall velocity (as estimated from the¹³CO emission), shows evidence of asymmetric infall, predominantly from the north and south. Close to the protostar, infall velocities appear to exceed free-fall velocities. Three-dimensional (3D) radiative transfer models, where the infall velocity is allowed to vary within the infall region, may explain the observed kinematics. Conclusions.The data suggest that a disk has started to form in B335 and that gas is falling towards that disk. However, kinematically-resolved line data towards the disk itself is needed to confirm the presence of a rotationally supported disk around this young protostar. The high infall velocities we measured are not easily reconcilable with a magnetic braking scenario, suggesting that there is a pressure gradient that allows the infall velocity to vary in the region.