Here is an obvious thing to say, since we often forget to look for the obvious when we study music: Music is historical. Musical traditions are built upon each other. Musical structures become increasingly complex or varied because they utilize earlier structures.
This means that we can often see the elements, templates or commonalities of simple musical structures within more complex ones. A good exercise is to take a harmonic reduction of a song to its basic elements. This can reveal an underlying structure that was masked by passing chords or various chord substitutions.
This can also be done with complex melodic phrases, where the main harmonic implications of the melody notes are isolated.
Another good exercise is to compare versions of an evergreen (a jazz or popular standard that has been played for decades and has many variations/iterations). A simple folk song or popular melody from the 1890s, for example, can be reharmonized with more modern jazz voicings, chromatic passing chords, syncopations and other effects, so that the original song is masked or only hinted at. You can often reverse engineer a modern song to hear the original simpler song structure it was based on.
I recommend to my jazz students analyzing Sonny Rollins’ songs in this way, such as Doxy, St. Thomas, Pent Up House. After reducing the song structure to its basic elements, you can build in your own complexities and variations in a way that matches your creativity and inspiration with your personal mastery level of music theory and technique.