  Boost-invariant dynamics of a strongly-coupled conformal plasma is studied in
the regime of early proper-time using the AdS/CFT correspondence. It is shown,
in contrast with the late-time expansion, that a scaling solution does not
exist. The boundary dynamics in this regime depends on initial conditions
encoded in the bulk behavior of a Fefferman-Graham metric coefficient at
initial proper-time. The relation between the early-time expansion of the
energy density and initial conditions in the bulk of AdS is provided. As a
general result it is proven that a singularity of some metric coefficient in
Fefferman-Graham frame exists at all times. Requiring that this singularity at
tau = 0 is a mere coordinate singularity without the curvature blow-up gives
constraints on the possible boundary dynamics. Using a simple Pade resummation
for solutions satisfying the regularity constraint, the features of a
transition to local equilibrium, and thus to the hydrodynamical late-time
regime, have been observed. The impact of this study on the problem of
thermalization is discussed.
