Overall, this work demonstrates the potential of CNN as a feature-engineering-free, high accuracy deep learning model to quantitatively link the complex structure-property relationships in composites with uniformly sized spherical particles. The strategy adopted in this study of combining the CNN-based deep learning model with a topology optimization algorithm can be generalized for accelerated prediction and optimization of nanocomposite properties, if sufficient computational or experimental material data are available to train the model. Further, such an approach to identify the optimal structures can be subsequently combined with inverse methods to determine the nanoparticle interactions or building blocks that promote self-assembly of the corresponding target structures. Broadly, our work demonstrates the potential of deep learning-based strategies to efficiently navigate the high-dimensional design space to discover/design materials with target properties.