The exploration of van der Waals (vdW) materials, renowned for their unique optical properties, is pivotal for advanced photonics. These materials exhibit exceptional optical anisotropy, both in-plane and out-of-plane, making them an ideal platform for novel photonic applications. However, the manual search for vdW materials with giant optical anisotropy is a labor-intensive process unsuitable for the fast screening of materials with unique properties. Here, we leverage geometrical and machine learning (ML) approaches to streamline this search, employing deep learning architectures, including the recently developed Atomistic Line Graph Neural Network. Within the geometrical approach, we clustered vdW materials based on in-plane and out-of-plane birefringence values and correlated optical anisotropy with crystallographic parameters. The more accurate ML model demonstrates high predictive capability, validated through density functional theory and ellipsometry measurements. Experimental verification with 2H-MoTe2 and CdPS3 confirms the theoretical predictions, underscoring the potential of ML in discovering and optimizing vdW materials with unprecedented optical performance.