Wideband terahertz (THz) massive multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) downlink systems have beam splitting which is a significant challenge. Delay-phase hybrid precoding, which combines digital precoding, analog precoding, and a time delay network, mitigates beam splitting. While alternating optimization (AO) frameworks are commonly used to optimize the design parameters of the individual components, difficulties are found specifically in designing the analog precoding matrix due to the non-convex constraints imposed by phase shifters in its implementation. Riemannian manifold optimization (RMO) can be a solution to design these phase shifts and achieve the desired performance but suffers from high computational and time complexity. To address this limitation, we created a novel, computationally efficient projected gradient descent (PGD)-based algorithm for designing the analog precoding in a delay-phase hybrid precoding architecture for the wideband THz massive MIMO-OFDM downlink system. Simulation results demonstrated that the proposed PGD-based algorithm achieves superior performance to that of the state-of-the-art RMO approach but with significantly lower computational complexity and reduced runtime.