Excitons in monolayer transition metal dichalcogenides (TMDs) have exceptionally large binding energies and dominate the optical properties of materials. Exploring the relaxation behavior of excitons is crucial for understanding the fundamental physics as well as the performance of TMD-based optoelectronic devices. However, ultrafast carrier dynamics is sensitive to the structural defects and surface conditions of TMDs, depending on the growth or transfer process. Here, we utilized pump-probe transient absorption (TA) spectroscopy with a white-light probe to investigate the dynamics of excitons in monolayer MoS2 synthesized by the metal sulfurization method. The sulfurization method was used for the fabrication of large-scale, continuous, and uniform thin films with a controllable number of layers. The excitation dynamics of the wafer-size monolayer MoS2 is found to be comparable to that of monolayer MoS2 flakes grown by chemical vapor deposition (CVD). The dominant processes of carrier relaxation in the monolayer MoS2 are exciton-exciton annihilation (hundreds of femtoseconds), the trapping of the excitons by surface states (a few picoseconds), and interband carrier-phonon scattering (tens of picoseconds). Moreover, the induced absorption due to mid-gap defects, which is often observed for samples fabricated by growth methods, such as CVD, is not observed for our continuous and uniform monolayer films. Understanding the charge carrier dynamics of the exciton in the scalable and uniform monolayer MoS2 can provide physical insights that are valuable in the design and development of complex 2D devices.