advance
晉 centers on moving forward or progressing: advancing in position, rank, or time.
晉 is an older form that combines elements suggesting reaching upward or forward. The modern simplified form is 晋. The exact historical development of the upper component is uncertain.
The upper part looks like two hands reaching up, and the bottom 日 suggests the sun or a goal. Picture hands stretching toward the sun, advancing upward.
For シン, imagine advancing with a confident shin (shin as in the front of the leg) step forward: shin -> シン, and each step moves you ahead.