In this paper we present optimized actuator trajectories, evolving in time and space, of non-inductive ramp-up scenarios for the Spherical Tokamak for Energy Production (STEP). These trajectories are computed by solving a non-linear, multi-objective, constrained, finite-time optimal control problem. A method unique to STEP ramp-up studies that provides an alternative to existing trajectory search strategies which rely on manually adjusting trajectories to reach a desired state. To navigate a nonlinear parameter space which is densely populated with local minima, we demonstrate an iterative objective function construction process whereby costs and constraints are included successively and re-optimized after each inclusion to improve convergence and feasibility. This method is particularity useful when the initial trajectory is far from the desired operating space. We use the RApid Plasma Transport simulatOR (RAPTOR) code to self-consistently solve four coupled, 1-D state equations; poloidal flux, electron temperature, ion temperature and electron density. Our STEP actuator trajectories lasting 1500s, consist of 8 Gaussian ECHCD beams distributed across the minor radius, a Deuterium/Tritium particle source and plasma current. We also introduce a modified transport Bohm-gyroBohm model and a new actuator module to RAPTOR which were required to adequately simulate the STEP operating scenarios.