  In this paper we investigate the vacuum stability of the non-minimally
coupled Standard-Model Higgs during a phase of kinetic domination following the
end of inflation. The non-minimal coupling to curvature stabilises the Higgs
fluctuations during inflation while driving them towards the instability scale
during kination, when they can classically overcome the potential barrier
separating the false electroweak vacuum from the true one at super-Planckian
field values. Avoiding the instability of the Standard-Model vacuum sets an
upper bound on the inflationary scale that depends both on the strength of the
non-minimal interaction and on the top quark Yukawa coupling. Classical vacuum
stability is guaranteed if the gravitationally-produced energy density is
smaller than the height of barrier in the effective potential. Interestingly
enough, thanks to the explosive particle production in the tachyonic phase, the
Higgs itself can be also appointed to the role of reheaton field responsible
for the onset of the hot Big Bang era, setting an additional lower bound on the
inflationary scale $\mathcal{H}_{\rm inf} \gtrsim 10^{5.5} \text{ GeV}$.
Overall, these constraints favour lower masses for the top quark, in agreement
with the current measurements of the top quark pole mass. We perform our
analysis semi-analytically in terms of the one-loop and three-loop running of
the Standard-Model Higgs self-coupling and make use of lattice-based parametric
formulas for studying the (re)heating phase derived in arXiv:2307.03774. For a
specific choice of $m_t=171.3 \text{ GeV}$ we perform also an extensive
numerical scanning of the parameter space via classical lattice simulations,
identifying stable/unstable regions and supporting the previous analytical
arguments. For this fiducial value, the heating of the Universe is achieved at
temperatures in the range $10^{-2} - 10^9 \text{ GeV}$.
