The COVID-19 pandemic has motivated scientists to delve deeper into this area and create cutting-edge biosensors that have the potential to enhance sensing beyond the current state of the art in terms of cost and accuracy. Several sensors for virus detection have been developed using chemical and electrochemical approaches as their foundations. Nevertheless, achieving high performance and accurate identification is not trivial. Surface plasmon resonance (SPR)-based optical biosensors are one method to capture very minute changes accurately via label-free sensing. This work offers a numerical approach for an ultra-sensitive multilayered SPR-based biosensor that uses angular interrogation in the near-infrared (NIR) region to detect the novel coronavirus (SARS-CoV-2). The multi-layered biosensor consists of a plasmonic metal, a dielectric layer (MgF₂), and optimized 2D nanomaterial (MoS₂) layers. In order to achieve high sensitivity, the figure of merit (FoM), and detection accuracy, the proposed plasmonic sensor was engineered using the transfer matrix method and finite element method after a thorough investigation. This includes the selection of plasmonic metal and optimization for the different layers. Using the strong binding efficiency of the MoS₂ layer and the high dielectric constant of the MgF₂ layer, the biosensor configuration comprising a glass prism/Al/Au/MgF₂/MoS₂/sensing sample is observed to exhibit the highest sensitivity of 372°/RIU, FoM of 1690 RIU^-1, and detection accuracy of 4.54 degree^-1. According to the investigation's findings, the proposed biosensor numerically exhibits excellent performance in the NIR region, making it easier to employ in the field of biomedical sensing applications.