While classical spintronics has traditionally relied on ferromagnetic metals as spin generators and spin detectors, spin-orbitronics exploits the interplay between charge and spin currents enabled by the spin-orbit coupling (SOC) in non-magnetic systems. An efficient spin-charge interconversion can be obtained through Spin Hall Effect and Inverse Spin Hall Effect in heavy metals such as Pt or Ta. Yet a more efficient conversion can be obtained by exploiting the direct and inverse Edelstein effects at interfaces where broken inversion symmetry induces a Rashba SOC. Although the simple Rashba picture of split parabolic bands is usually used to interpret such experiments, it fails to explain the largest conversion effects and their relation to the actual band-structure. Here, we demonstrate a giant spin-to-charge conversion effect by means of Spin Pumping FMR in an interface-engineered high-carrier-density SrTiO3 two-dimensional electron gas. We use angle-resolved photoemission and Boltzmann calculations to map its peculiar gate dependence. We show that the conversion process is amplified by enhanced Rashba-like splitting due to orbital mixing, and in the vicinity of avoided band crossings with topologically non-trivial order. Our results indicate that oxide 2DEGs are strong candidates for spin-based information readout in novel memory and transistor designs. In parallel, they confirm the promise of topology as a new ingredient to expand the scope of complex oxides for spintronics.