  The symmetric mass generation (SMG) phase is an insulator in which a
single-particle gap is intrinsically opened by the interaction, without
involving symmetry spontaneously breaking or topological order. Here, we
perform unbiased quantum Monte-Carlo simulation and systematically investigate
a bilayer fermionic model hosting Fermi surface SMG in the strongly interacting
regime. With increasing interaction strength, the model undergoes a quantum
phase transition from an exciton insulator to an SMG phase, belonging to the
(2+1)-dimensional O(4) universality class. We access the spectral properties of
the SMG phase, resembling a Mott insulating phase with relatively flat
dispersion and pronounced spectral broadening. The dispersion of Green's
function zeros is extracted from spectral function, featuring a surface at zero
frequency precisely located at the original non-interacting Fermi surface,
which constitutes a hallmark of the Fermi surface SMG phase. The bilayer model
we study is potentially relevant to the newly discovered high-$T_c$
superconductor $\rm{La}_3 \rm{Ni}_2 \rm{O}_7$. Our results in SMG phase
qualitatively capture the salient features of spectral function unveiled in
recent ARPES experiments, shedding new insight on the underlying physics of
$\rm{La}_3 \rm{Ni}_2 \rm{O}_7$.
