This letter presents deep learning (DL) based non-orthogonal random access (NORA) where multiple nodes utilizing the identical preamble simultaneously transmit data over the same time-frequency resources. Effective power control algorithms are essential for the NORA, however, only partial information of channels such as the timing advance (TA) is available. This poses challenges for existing algorithms requiring full channel knowledge. We propose unsupervised DL-based power control schemes which maximize the minimum rate based only on the TA information. Numerical results verify the effectiveness of the proposed DL-based NORA over conventional methods.