Recently, there has been a surge in use of electric propulsion to transfer satellites to the geostationary Earth orbit (GEO). Traditionally, the transfer times to reach GEO using all-electric propulsion are obtained by solving challenging trajectory optimization problems that naturally do not lend themselves to incorporation within deep reinforcement learning (DRL) framework to solve trajectory planning problems in near real-time. The operation of DRL, as typically used in trajectory planning, relies on a Q-value. In the electric orbit-raising problem under consideration in this paper, this Q-Value requires computation of transfer time in near real-time to have practical DRL training times. This work proposes to design and evaluate a machine learning (ML) framework, focusing on deep neural networks (DNNs), to predict the transfer time to assist in Q-value determination instead of solving traditional orbit-raising optimization problems. To this end, we investigate different architectures for DNNs to determine a suitable DNN configuration that can predict the transfer time for each of the mission scenarios with high accuracy. Experimental results indicate that our designed DNNs can predict the transfer time for different scenarios with an accuracy of over 99.97%. To verify the efficacy of our designed DNNs for predicting transfer time that is required for Q-value estimation, we also compare the results from our designed DNNs with the contemporary ML algorithms, such as support vector machines, random forests, and decision trees for regression. Experimental results indicate that our best-performing DNNs can provide an improvement in the mean error of transfer time prediction by up to 14.05× for non-planar transfers and up to 254× for planar transfers as compared to contemporary ML algorithms.