Exciton-polariton bound states in the continuum (BICs) are hybrid quasiparticles formed under strong coupling between optical BICs and excitons. However, as BICs have vanishing line width, it is impossible to excite them directly with external optical sources. Consequently, their infinite lifetime cannot be efficiently utilized for coherently driven polaritonic applications. In this Letter, we show that the nonlinear nature of exciton-polaritons enables an efficient coherent excitation of the BIC via optical parametric oscillation (OPO). Thanks to the enhanced lifetime of the BIC, the requirement for the pump and the idler to be in resonance with a polariton mode is lifted. This allows the OPO process to take place over a large range of pump wavevectors and energy, thereby efficiently populating the polariton BICs.