The main characteristics of Solar-C_EUVST are the high temporal and high spatial resolutions over a wide temperature coverage. In order to realize the instrument for meeting these scientific requirements under size constraints given by the JAXA Epsilon vehicle, we examined four-dimensional optical parameter space of possible solutions of geometrical optical parameters such as mirror diameter, focal length, grating magnification, and so on. As a result, we have identified the solution space that meets the EUVST science objectives and rocket envelope requirements. A single solution was selected and used to define the initial optical parameters for the concept study of the baseline architecture for defining the mission concept. For this solution, we optimized the grating and geometrical parameters by ray tracing of the Zemax software. Consequently, we found an optics system that fulfills the requirement for a 0.4” angular resolution over a field of view of 100" (including margins) covering spectral ranges of 170-215, 463-542, 557-637, 690-850, 925-1085, and 1115-1275 A. This design achieves an effective area 10 times larger than the Extreme-ultraviolet Imaging Spectrometer onboard the Hinode satellite, and will provide seamless observations of 4.2-7.2 log(K) plasmas for the first time. Tolerance analyses were performed based on the optical design, and the moving range and step resolution of focus mechanisms were identified. In the presentation, we describe the derivation of the solution space, optimization of the optical parameters, and show the results of ray tracing and tolerance analyses.