If you can link to a specific video of "Starlings" and identify the timestamp when the particular sound is played, it might help.
Speaking in general, the first step is to identify the type of wave(s) used for the oscillator(s)-- sine, saw, triangle, pulse, etc. If two or more oscillators generating different waveforms are being used, it can be trickier to identify them, especially if one is retriggering or modulating the other. The oscillators can also be tricky to get right because of things like octave tuning, semitone tuning, and fine tuning of each oscillator, as well as their relative amplitudes.
Then go after the ADSR envelope to get the basic shape/action of the notes.
And finally, play with the filter controls, the effects (reverb, chorus, etc.), and-- if pertinent-- things like glide or portamento.
Sometimes it helps to just identify the particular synth being used, since different synths might use different types of synthesis, or offer specific waveforms or other features, and information like that might help with narrowing things down.
Or you might luck out and find an interview where the synth player was asked about a particular sound in a particular song.