I've been working with the David Lucas Burge Ear Training Super Courses for years now and I'm pretty sure I've figured it out.

What I do is listen for the subtle hisses and static sounds in the air.

Then I think you make listening in that way a daily habit for a few minutes a day until it becomes habit and routine.

So I listen for the subtle undertone and overtone signature patterns instead of the surface level timbre sounds.