We present a novel methodology to identify topologically non-trivial materials based on band inversion induced by spin-orbit coupling (SOC) effect. Specifically, we compare the density functional theory (DFT) based wavefunctions with and without spin-orbit coupling and compute the 'spin-orbit-spillage' as a measure of band-inversion. Due to its ease of calculation, without any need for symmetry analysis or dense k-point interpolation, the spillage is an excellent tool for identifying topologically non-trivial materials. Out of 30000 materials available in the JARVIS-DFT database, we applied this methodology to more than 4835 non-magnetic materials consisting of heavy atoms and low bandgaps. We found 1868 candidate materials with high-spillage (using 0.5 as a threshold). We validated our methodology by carrying out conventional Wannier-interpolation calculations for 289 candidate materials. We demonstrate that in addition to Z2 topological insulators, this screening method successfully identified many semimetals and topological crystalline insulators. Importantly, our approach is applicable to the investigation of disordered or distorted as well as magnetic materials, because it is not based on symmetry considerations. We discuss some individual example materials, as well as trends throughout our dataset, which is available at the websites: https://www.ctcms.nist.gov/~knc6/JVASP.html and https://jarvis.nist.gov/ .