  We chart a singular landscape in the temporal domain of the inviscid Burgers
equation in one space dimension for sine-wave initial conditions. These so far
undetected complex singularities are arranged in an eye shape centered around
the origin in time. Interestingly, since the eye is squashed along the
imaginary time axis, complex-time singularities can become physically relevant
at times well before the first real singularity -- the pre-shock. Indeed,
employing a time-Taylor representation for the velocity around $t=0$, loss of
convergence occurs roughly at 2/3 of the pre-shock time for the considered
single- and multi-mode models. Furthermore, the loss of convergence is
accompanied by the appearance of initially localized resonant behaviour which,
as we claim, is a temporal manifestation of the so-called tyger phenomenon,
reported in Galerkin-truncated implementations of inviscid fluids [Ray et al.,
Phys. Rev. E 84, 016301 (2011)]. We support our findings of early-time tygers
with two complementary and independent means, namely by an asymptotic analysis
of the time-Taylor series for the velocity, as well as by a novel singularity
theory that employs Lagrangian coordinates.
  Finally, we apply two methods that reduce the amplitude of early-time tygers,
one is tyger purging which removes large Fourier modes from the velocity, and
is a variant of a procedure known in the literature. The other method realizes
an iterative UV completion, which, most interestingly, iteratively restores the
conservation of energy once the Taylor series for the velocity diverges. Our
techniques are straightforwardly adapted to higher dimensions and/or applied to
other equations of hydrodynamics.
