Recent studies show that volume fractions φ(J) at the jamming transition of frictionless hard spheres and disks are not uniquely determined but exist over a continuous range. Motivated by this observation, we numerically investigate the dependence of φ(J) on the initial configurations of the parent fluid equilibrated at a volume fraction φ(eq), before compressing to generate a jammed packing. We find that φ(J) remains constant when φ(eq) is small but sharply increases as φ(eq) exceeds the dynamic transition point which the mode-coupling theory predicts. We carefully analyze configurational properties of both jammed packings and parent fluids and find that, while all jammed packings remain isostatic, the increase of φ(J) is accompanied with subtle but distinct changes of local orders, a static length scale, and an exponent of the finite-size scaling. These results are consistent with the scenario of the random first-order transition theory of the glass transition.