As demand grows for real-time diagnostics and control in mirror structure and optical system design, traditional computation-heavy methods face efficiency bottlenecks. To address this, we propose OMS-DNN, a fully data-driven deep learning framework that replaces resource-intensive finite element analysis and ray tracing, while integrating optimization algorithms for forward design. OMS-DNN models complex nonlinear relationships using deep neural networks and captures parameter topologies through a graph convolutional network (GCN). We evaluate OMS-DNN on large-scale datasets, including 20,000 structural and 100,000 Three-Mirror Anastigmat (TMA) optical design samples. It achieves mean absolute percentage errors (MAPE) of 0.98%, 4.09%, and 1.66% across three key metrics. To meet forward design requirements, we integrated the proposed architecture with an optimization algorithm. Experimental results demonstrate that our method can rapidly generate constraint-compliant parameter design solutions tailored to various needs, thereby lowering the entry barrier for designers. These findings validate the effectiveness of OMS-DNN and its potential to transform traditional design workflows.