This might sound a bit random, but Cyberpunk 2077 has this sort of warmup sound that plays through the game startup sequence that always gets me relaxed or psyched up to play. Another example is the title song in Trails from Zero. Calms me every time.
Whether it’s a sound effect, music, or a loading screen, is there a game that does this for you immediately when you open it?
Probably Katamari Damacy Reroll. The music is so whimsical, and loading your save at the startup screen uses the unique movement (double joystick) so I’m already using the controls before actually playing.