Using the weak-noise theory, we evaluate the probability distribution P(H,t) of large deviations of height H of the evolving surface height h(x,t) in the Kardar-Parisi-Zhang (KPZ) equation in one dimension when starting from a flat interface. We also determine the optimal history of the interface, conditioned on reaching the height H at time t. We argue that the tails of P behave, at arbitrary time t>0, and in a proper moving frame, as -P∼ |H|^5/2 and ∼ |H|^3/2. The 3/2 tail coincides with the

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... symptotic of the Gaussian orthogonal ensemble Tracy-Widom distribution, previously observed at long times.