advance, proceed, progress, promote
進 centers on forward movement: advancing physically, making progress in a task, or promoting someone to a higher position.
to advance; to go forward
to advance; to move forward; to put (a clock, watch) forward
evolution
moving forward (e.g. of a vehicle); onward movement
propulsion; drive
advance (into a new market, industry, etc.); expansion (into); launch (into); entering; making inroads (into)
promotion; acceleration; encouragement; facilitation; spurring on
progress; advance; improvement; development
advanced; developed
advancing to the next stage of education; going on to (high school, college, etc.)
advance; moving forward; progress
route; course; path
promotion; advancement; rising in rank
progress; development
advance; charge
march; parade
progress; advance; making (good) progress
departure (from a base); takeoff; launch
entry; going into; approach
making rapid progress; making great advances; rush; dash; onslaught
one's junior; younger generation; next generation
concentration; diligence; devotion
going straight on; going straight ahead
promoting; increase; advance
進 combines 辶 (movement) with 隹, which likely contributes the sound and originally depicted a bird. The idea is a bird moving forward, hence advancing.
The movement radical 辶 wraps around 隹, a bird. Picture a bird striding forward, making steady progress.
For シン, imagine a shiny new promotion: shin -> シン, and you advance in your career.