  Previous observations of B335 have presented evidence of ongoing infall in
various molecular lines, e.g., HCO$^+$, HCN, CO. There have been no confirmed
observations of a rotationally supported disk on scales greater than ~12~au.
The presence of an outflow in B335 suggests that also a disk should be present
or in 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. We use
high angular resolution $^{13}$CO data from ALMA, and combine it with
shorter-baseline archival data to produce a high-fidelity image of the infall
in B335. We also revisit the imaging of high-angular resolution Band 6
continuum data to study the dust distribution in the immediate vicinity of
B335. 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 the
$^{13}$CO emission), shows evidence of asymmetric infall, predominantly from
the north and south. Close to the protostar, infall velocities appear to exceed
free-fall velocities. 3D radiative transfer models, where the infall velocity
is allowed to vary within the infall region, can explain the observed
kinematics. The data suggests 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 measured high infall velocities
are not easily reconcilable with a magnetic braking scenario and suggest that
there is a pressure gradient that allows the infall velocity to vary in the
region.
