Based on the current experimental data, the Standard Model predicts that the
current vacuum state of the Universe is metastable, leading to a non-zero rate
of vacuum decay through nucleation of bubbles of true vacuum. Our existence
implies that there cannot have been any such bubble nucleation events anywhere
in our whole past lightcone. We consider a minimal scenario of the Standard
Model together with Starobinsky inflation, using three-loop renormalization
group improved Higgs effective potential with one-loop curvature corrections.
We show that the survival of the vacuum state through inflation places a lower
bound $\xi \gtrsim 0.1$ on the non-minimal Higgs curvature coupling, the last
unknown parameter of the Standard Model. This bound is significantly stronger
than in single field inflation models with no Higgs-inflaton coupling. It is
also sensitive to the details of the dynamics at the end of inflation, and
therefore it can be improved with a more detailed study of that period.