Self-assembly processes in biological and synthetic biomolecular systems are often governed by the spatial separation of biochemical processes. While previous work has focused on optimizing self-assembly through fine-tuned reaction parameters or using phase-separated liquid compartments with fast particle exchange, the role of slow intercompartmental exchange remains poorly understood. Here, we demonstrate that slow particle exchange between reaction domains can enhance self-assembly efficiency through a cooperative mechanism: delay-facilitated assembly. Using a minimal model of irreversible self-assembly in two compartments with distinct reaction and exchange dynamics, we identify scenarios where slow particle exchange maximizes yield and minimizes assembly time for given suboptimal reaction dynamics, even under conditions where isolated compartments would fail to facilitate any self-assembly. The mechanism relies on a separation of timescales between intracompartmental reactions and intercompartmental exchange and is robust across a wide range of geometries, including spatially extended domains with diffusive transport. We demonstrate that this effect enables geometric control of self-assembly processes through compartment volumes and exchange rates, eliminating the need for fine-tuning local reaction rates. These results offer a conceptual framework for leveraging spatial separation in synthetic self-assembly design and suggest that biological systems may use slow particle exchange to improve assembly efficiency.