I usually try to start with the right sound.
If I can make the mix and instruments sound the right way, I find that the music becomes more fluid and easier to pick out that starting musical thread.
I do a lot of active listening by studying musical and mixing idiosyncracies that make up a particular style of the pieces I use as reference. I also play around a lot with different styles.
It's a time investment - the more you do this, the easier it becomes.