  The thermodynamic uncertainty relation (TUR) describes a trade-off relation
between nonequilibrium currents and entropy production and serves as a
fundamental principle of nonequilibrium thermodynamics. However, currently
known TURs presuppose either specific initial states or an infinite-time
average, which severely limits the range of applicability. Here we derive a
finite-time TUR valid for arbitrary initial states from the Cram\'er-Rao
inequality. We find that the variance of an accumulated current is bounded by
the instantaneous current at the final time, which suggests that ``the boundary
is constrained by the bulk". We apply our results to feedback-controlled
processes and successfully explain a recent experiment which reports a
violation of a modified TUR with feedback control. We also derive a TUR that is
linear in the total entropy production and valid for discrete-time Markov
chains with non-steady initial states. The obtained bound exponentially
improves the existing bounds in a discrete-time regime.
