While spintronics has traditionally relied on ferromagnetic metals as spin generators and detectors, spin–orbitronics exploits the efficient spin–charge interconversion enabled by spin–orbit coupling in non-magnetic systems. Although the Rashba pic- ture of split parabolic bands is often used to interpret such experiments, it fails to explain the largest conversion effects and their relationship with the electronic structure. Here, we demonstrate a very large spin-to-charge conversion effect in an inter- face-engineered, high-carrier-density SrTiO3 two-dimensional electron gas and map its gate dependence on the band structure. 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 two-dimensional electron gases are strong candidates for spin-based information readout in new memory and transistor designs. Our results also emphasize the promise of topology as a new ingredient to expand the scope of complex oxides for spintronics.