Engineering an array of precisely located cavity-coupled active media poses a major experimental challenge in the field of hybrid integrated photonics. We deterministically position solution processed colloidal quantum dots (QDs) on high quality-factor silicon nitride nanobeam cavities and demonstrate light-matter coupling. By lithographically defining a window on top of an encapsulated cavity that is cladded in a polymer resist, and spin coating QD solution, we can precisely control the placement of the QDs, which subsequently couple to the cavity. We show that the number of QDs coupled to the cavity can be controlled by the size of the window. Furthermore, we demonstrate Purcell enhancement and saturable photoluminescence in this QD-cavity platform. Finally, we deterministically position QDs on a photonic molecule and observe QD-coupled cavity super-modes. Our results pave the way for controlling the number of QDs coupled to a cavity by engineering the window size, and the QD dimension, and will allow advanced studies in cavity enhanced single photon emission, ultralow power nonlinear optics, and quantum many-body simulations with interacting photons.