Atomically thin group-VI transition metal dichalcogenides have garnered significant attention for potential electronic and optoelectronic applications. These two-dimensional (2D) monolayer materials exhibit noteworthy features driven by the inversion symmetry and the spin-orbit coupling (SOC) effects. Through Floquet engineering, the impact of SOC on the Floquet oscillations in these 2D materials has been elucidated using theoretical and numerical methods. The study reveals the substantial effect of SOC coupling on the Rabi frequency and the Bloch-Siegert shift phenomenon. Furthermore, it becomes evident that SOC plays a pivotal role in the quantum mechanical collapse and revival phenomenon within the Floquet framework. The observed offset Floquet oscillations are solely contributed by the gap term and the spin-orbit interaction parameter. In the zero-photon limit, a corresponding phenomenon called as vacuum Floquet oscillation also occurs.