Integrated photon-pair sources based on spontaneous parametric down conversion (SPDC) in novel high-${\chi }^{(2)}$ materials are used in quantum photonic systems for quantum information processing, quantum metrology, and quantum simulations. However, the need for extensive fabrication process development and optimization of dry-etching processes significantly impedes the rapid exploration of different material platforms for low-loss quantum photonic circuits. Recently, bound states in the continuum (BICs) have emerged as a promising approach for realizing ultralow-loss integrated photonic circuits without requiring an etching process. Previous realizations of BIC photonic circuits have, however, been limited primarily to the classical regime. Here, we explore the BIC phenomena in the quantum regime and show that the etchless BIC platform is suitable for use in integrated entangled photon-pair sources based on the SPDC process in high-${\chi }^{(2)}$ materials. Using lithium niobate as an example, we demonstrate photon-pair generation at telecommunication wavelengths, attaining a maximum internal generation rate of 3.46 MHz, a coincidence-to-accidental ratio of 5773, and an experimental two‐photon interference visibility of 94%. Our results demonstrate that the BIC platform can be used for quantum photonic circuits, and this will enable the rapid exploration of different emerging ${\chi }^{(2)}$ materials for possible use in integrated quantum photonics in the future.