Optimal transmission switching (OTS) improves optimal power flow (OPF) by selectively opening transmission lines, but its mixed-integer formulation increases computational complexity, especially on large grids. To deal with this, we propose a dispatch-aware deep neural network (DA-DNN) that accelerates DC-OTS without relying on pre-solved labels. DA-DNN predicts line states and passes them through a differentiable DC-OPF layer, using the resulting generation cost as the loss function so that all physical network constraints are enforced throughout training and inference. In addition, we adopt a customized weight-bias initialization that keeps every forward pass feasible from the first iteration, which allows stable learning on large grids. Once trained, the proposed DA-DNN produces a provably feasible topology and dispatch pair in the same time as solving the DCOPF, whereas conventional mixed-integer solvers become intractable. As a result, the proposed method successfully captures the economic advantages of OTS while maintaining scalability.