So I was trying to get a result that resembles the colored powder used at Holi festivals. I played around with a lot of settings, but didn’t manage to get anything close to this.
I would like something like this, An object emerging from colors,
Maybe you could create an object in the shape of the thing you want to appear. Create a particle system to emit for just one frame, emitting from volume rather than surface. Use the same material as your main particle system and set emitter to invisible.
That way the shape would appear briefly as a denser cloud within your particles before appearing to dissipate among them.