Here’s another method which has a lot do with the fact that I don’t read or write music notation.
I often start developing ideas by exploring different (often non-standard) chords on guitar or even piano (which I cannot really play). When I find some progressions which sound interesting to me I record these and I then start developing themes on top of the progression. The main thing for me is that chord progression needs to sound like you would like play something on top that. It can be non-standard chords or it could be standard chords with some rhythmic idea or with some little twist. I think the main thing is free exploration of sounds.
This little piece is an example of the above method:
I do the reverse too, i.e. develop a theme or melody first. Also this often happens by some kind of improvisational approach.