The development of digital twins to represent the optical transport network might enable multiple applications for network operation, including automation and fault management. In this work, we propose a deep-learning-based digital twin for the optical time domain, named OCATA. OCATA is based on the concatenation of deep neural network (DNN) modeling of optical links and nodes, which facilitates representing lightpaths. The DNNs model linear and nonlinear noise, as well as optical filtering. Additional DNN-based models are proposed to extract useful lightpath metrics, such as lightpath length, number of optical links, and nonlinear fiber parameters. OCATA exhibits low complexity, thus making it ideal for real-time applications. Illustrative results for the application of OCATA to disaggregated and mixed disaggregated-proprietary optical network scenarios reveal remarkable accuracy.