Ultrasound is an adjunct tool to mammography that can quickly and safely aid physicians with diagnosing breast abnormalities. Clinical ultrasound often assumes a constant sound speed to form B-mode images for diagnosis. However, the various types of breast tissue, such as glandular, fat, and lesions, differ in sound speed. These differences can degrade the image reconstruction process. Alternatively, sound speed can be a powerful tool for identifying disease. To this end, we propose a deep-learning approach for sound speed estimation from in-phase and quadrature ultrasound signals. First, we develop a large-scale simulated ultrasound dataset that generates quasi-realistic breast tissue by modeling breast gland, skin, and lesions with varying echogenicity and sound speed. We developed a fully convolutional neural network architecture trained on a simulated dataset to produce an estimated sound speed map from inputting three complex-value in-phase and quadrature ultrasound images formed from plane-wave transmissions at separate angles. Furthermore, thermal noise augmentation is used during model optimization to enhance generalizability to real ultrasound data. We evaluate the model on simulated, phantom, and in-vivo breast ultrasound data, demonstrating its ability to accurately estimate sound speeds consistent with previously reported values in the literature. Our simulated dataset and model will be publicly available to provide a step towards accurate and generalizable sound speed estimation for pulse-echo ultrasound imaging.