  Many proposals to generate a time-reversal invariant topological
superconducting phase are based on imposing a $\pi$ phase difference between
the superconducting leads proximitizing a nanostructure. We show that this
phase can be induced on a thin film of a topological insulator like
Bi$_2$Se$_3$ in proximity to a single s-wave superconductor. In our analysis we
take into account the parity degree of freedom of the electronic states which
is not included in effective Dirac-like surface theories. We find that the
topological phase can be reached when the induced interparity pairing dominates
over the intraparity one. Application of an electric field perpendicular to the
film extends the range of parameters where the topological phase occurs.
