During research, domain experts often ask analytical questions whose answers require integrating data from a wide range of web sources. Thus, they must spend substantial effort searching, extracting, and organizing raw data before analysis can begin. We formalize this process as the SODIUM task, where we conceptualize open domains such as the web as latent databases that must be systematically instantiated to support downstream querying. Solving SODIUM requires (1) conducting in-depth and specialized exploration of the open web, which is further strengthened by (2) exploiting structural correlations for systematic information extraction and (3) integrating collected information into coherent, queryable database instances. To quantify the challenges in automating SODIUM, we construct SODIUM-Bench, a benchmark of 105 tasks derived from published academic papers across 6 domains, where systems are tasked with exploring the open web to collect and aggregate data from diverse sources into structured tables. Existing systems struggle with SODIUM tasks: we evaluate 6 advanced AI agents on SODIUM-Bench, with the strongest baseline achieving only 46.5% accuracy. To bridge this gap, we develop SODIUM-Agent, a multi-agent system composed of a web explorer and a cache manager. Powered by our proposed ATP-BFS algorithm and optimized through principled management of cached sources and navigation paths, SODIUM-Agent conducts deep and comprehensive web exploration and performs structurally coherent information extraction. SODIUM-Agent achieves 91.1% accuracy on SODIUM-Bench, outperforming the strongest baseline by approximately 2 times and the weakest by up to 73 times.