  Growth of graphene on monolayer transition-metal dichalcogenides presents
opening on band gap and giant spin-orbit coupling which paves the way to
achieve a useful hybrid structure for electronics and spintronics applications.
Increase of the atomic number of transition-metal results in a large SOC, where
eventually a band inversion appears in graphene-$WSe_2$. We consider
superconductor induction by proximity effect to the graphene-TMDC hybrid
structure. As a necessity of formalism, we introduce a proper time-reversal and
particle-hole symmetry operators, under which the $8 \times 8$
Dirac-Bogoliubov-de Gennes low-energy effective Hamiltonian is invariant.
Resulting superconducting electron-hole excitations shows that, the essential
dynamical parameters $\lambda_I^{A,B}$ and $\lambda_R$ have significant effect
on superconducting excitations and, specifically, subgap energy. Dependence of
the superconducting energy excitation on chemical potential is explored. The
signature of spin triplet $p$-wave pairing symmetry in the system is found to
increase the subgap superconducting energy, in comparing to $s$-wave symmetry.
