  We determine the optimal conditions to achieve topological superconducting
phases having spin-singlet pairing for a planar nanowire with finite lateral
width in the presence of an in-plane external magnetic field. We employ a
microscopic description that is based on a three-band electronic model
including both the atomic spin-orbit coupling and the inversion asymmetric
potential at the interface between oxide band-gap insulators. We consider
amplitudes of the pairing gap, spin-orbit interactions and electronic
parameters that are directly applicable to nanowires of LaAlO$_3$-SrTiO$_3$.
The lateral confinement introduces a splitting of the $d$-orbitals that alters
the orbital energy hierarchy and significantly affects the electron filling
dependence of the topological phase diagram. Due to the orbital directionality
of the $t_{2g}$-states, we find that in the regime of strong confinement the
onset of topological phases is pinned at electron filling where the quasi flat
heavy bands start to get populated. The increase of the nanowire thickness
leads to a changeover from sparse-to-dense distribution of topologically
non-trivial domains which occurs at the cross-over associated to the orbital
population inversion. These findings are corroborated by a detailed analysis of
the most favorable topological superconducting phases in the electron
doping-magnetic field plane highlighting the role of orbital selective
confinement.
