In wideband sub-Terahertz (sub-THz) massive multiple-input multiple-output (MIMO) communication systems, the beam squint effect manifests as a substantial degradation in array gain. To mitigate the aforementioned beam squint effect, a hybrid precoding approach leveraging both true-time delay (TTD) and phase shifters (PS) has been proposed. However, existing methods operate under the assumption that the TTD device can generate any desired time delay value. These methods subsequently design the TTD precoder while fixing the PS precoder. This work presents a novel optimization framework for the joint TTD and PS precoder design, incorporating realistic time delay constraints for each TTD device. Unlike previous methods, our framework does not rely on the unbounded time delay assumption and optimizes the TTD and PS values jointly to cope with the practical limitations. Furthermore, within the context of our proposed framework, we mathematically determine the minimum number of TTD devices necessitated to achieve a predetermined target array gain. Simulations confirm the proposed approach exhibits performance improvement, guarantees array gain, and achieves computational efficiency.