  We investigate the non-equilibrium dynamics of an impurity coupled to a
Bose-Einstein condensate, systematically compared with recent experimental
results [M. G. Skou et al., Nat. Phys. (2021)]. The dynamics of the impurity is
tracked down by using a time-dependent variational coherent ansatz. For weak
coupling between the impurity and the bath, analytical expressions for the
time-dependent overlap (or contrast) are derived, matching quite well with
previous findings obtained within a master equation approach. For strong
coupling instead, the variational ansatz provides a good quantitative
description of the polaron dynamics, in particular, in signaling the transition
from the few to the many-body correlated regime where polarons are expected to
form.
