Lensless, interferenceless coded aperture correlation holography (LI-COACH) is an incoherent computational optical technique for three-dimensional (3D) imaging. In direct imaging, the image of the object is generated by a lens, whereas the LI-COACH is an indirect imaging technique that consists of two steps: one-time point spread hologram (PSH) training and then many times imaging of multiple-point objects. In the one-time training step, a point object moves in the object space along the optical axis. Light emitted from the point is modulated by a quasi-random phase mask, and the PSH library is recorded. In the imaging step, an object is mounted within the axial boundaries of the PSH library, and the object holograms are recorded using the same quasi-random phase masks. The 3D image of the object is reconstructed by the cross correlation of the object holograms with the PSH library. In this study, the entire PSH library is digitally synthesized from a single PSH, recorded at one plane only. The recorded PSH is scaled by magnification factors corresponding to the various axial planes. The reconstruction results from the synthetic PSH library are comparable with those from the recorded PSH library. The proposed approach can reduce the time of the training step in LI-COACH.