Solid-oxide fuel-cell (SOFC)/gas-turbine hybrid systems possess the capacity for unprecedented performances, such as electric efficiencies nearly twice that of conventional heat engines at variable scale power ratings inclusive of distributed generation; however, reliably integrating such technologies is critical. Dynamic operability challenges ranging from surge-stall events in the turbomachinery to threatening thermally induced stresses within the fuel cells are formidable. An effective means of characterizing the operability of such systems requires a simulation approach of high fidelity yet reduced sacrificial risk associated with empirical investigation of SOFC stacks. Accordingly, a unique cyber-physical simulation (CPS) was developed inclusive of a spatio-temporal SOFC computational model interfaced with a retrofitted turbine. The model had an extensively broad operating range, as compared to other models that have been developed, with the capability to characterize inert heating, electrochemical start-up, and on and off design operation. A comprehensive parametric characterization was done for initial electrochemical light-off with variability in compressor by-pass valve position and initial fuel-cell load for both closed loop and open loop (OL) turbine speed system configurations. The impact of cold-air (CA) by-pass, as well as initial fuel-cell load on system parameters that directly affect SOFC operation, such as inlet air temperature, pressure, and flow, along with turbine speed and thermal effluent dynamics are presented and discussed. Additionally, the full spatio-temporal capability was exhibited and utilized in examining the impact of electrochemical start-up upon SOFC temperature and temperature gradients as a result of local current density and by-product heat distribution. Ultimately, a comprehensive parametric study, characterizing SOFC and hybrid system response to electrochemical start-up along the decision variable values of initial fuel-cell load, as well as CA by-pass valve position, was completed; this illustrated an advanced simulation platform for gathering such insights about developmental fuel-cell systems.