The short wavelength of terahertz (THz) waves makes the acceleration of electrons, from typical electron gun energies to fully relativistic energies, challenging due to the need to match the velocities over comparably long distances. However, the inherent laser synchronisation of a photogun to the THz drive laser offers significant advantage in applications where timing is critical. We present a novel design process for high-gradient THz-driven dielectric-lined waveguide injectors and demonstrate designs for rectangular and cylindrical geometries. These structures utilize novel tapering and stepping schemes to manipulate the phase velocity, controlling the position of the electron bunch relative to the phase of the accelerating field. We demonstrate a hybrid optimisation method utilizing firstly a multi-objective genetic algorithm based on analytic models of the waveguide accelerating modes, and then high-detail particle-in-cell simulations. Our example designs achieve electron acceleration from 100 keV to 1 MeV over a distance of 20 mm by interacting with a multicycle 0.5 mJ, 0.2 THz pulse, paving the way for the realisation of THz-based injectors. The exit beam shows excellent beam quality with 50 fs bunch lengths, sub 0.5% energy spread and emittances of under 0.15 μrad. We also present an analysis of the robustness of the designs to errors in machining and operational parameters demonstrating the feasibility of the concept. We show that using multi-objective genetic algorithm optimization and robust design process, we can achieve high-quality 1 MeV beams.