  We continue the study of dipole cosmology framework put forward in
\cite{Krishnan:2022qbv}, a beyond FLRW setting that has a preferred direction
in the metric which may be associated with a cosmological tilt, a cosmic
dipole. In this setup the shear and the tilt can be positive or negative given
the dipole direction. Here we focus on the behaviour near the Big Bang (BB) in
this setting. We first analyze a single fluid model with a generic constant
equation of state $w$. In this case shear and the tilt have the same signs.
While details of the behavior near the BB depends on $w$ and the other initial
conditions, we find that when the shear is negative we have a shear dominated
BB singularity, whereas for a positive shear we have a much milder singularity,
the whimper singularity \cite{Ellis:1974ug}, at which the tilt blows up while
curvature invariants remain finite. We also analyze dipole $\Lambda$CDM model
and explore its near BB behavior, which besides the shear has two tilt
parameters, one for radiation and one for the pressureless matter. For positive
(negative) shear we again find whimper (curvature) singularity. Moreover, when
the tilt parameters have opposite signs, the shear can change sign from
negative to positive in the course of evolution of the Universe. We show that
the relative tilt of the radiation and the matter generically remains sizeable
at late times.
