In this study, we investigate the electronic structure and topological properties of the compound SrS⁢i₂ using angle-resolved photoemission spectroscopy (ARPES), electrical transport measurements, and ab initio calculations. In contrast to recent theoretical predictions that SrS⁢i₂ is a Weyl semimetal with robust Weyl nodes and Fermi arcs, our ARPES measurements on undoped and Ca-doped SrS⁢i₂ single crystals show no evidence of the predicted Weyl fermions or Fermi arcs at ambient pressure. Instead, ARPES and transport data show that SrS⁢i₂ is a narrow-gap semiconductor at ambient conditions. Our hybrid functional calculations also find a small band gap, in agreement with experiments. However, by applying external pressure, we induce a topological phase transition where the electronic bands overlap and Weyl nodes appear, as confirmed by transport measurements and calculations. Interestingly, we also observe a pressure-induced superconducting transition above 20 GPa. Our results establish SrS⁢i₂ as a platform to study the interplay between topological states and superconductivity driven by external pressure. Importantly, our results challenge the previously predicted intrinsic Weyl semimetallic nature of SrS⁢i₂ and highlight the need for combined experimental and advanced computational approaches to correctly describe the complex electronic structures in topological materials.