Since the medium in which light propagates is spacetime, would light be able to exist if spacetime did not exist? Is this like one of those chicken/egg problems, or can light be thought of as a legitimately independent entity? This might be bordering on an philosophical question, so if it is, let me know and I'll delete it.
Space-time is not really a "medium", it does not vibrate when a light wave is passing through. It just gives a reference of positions and instants in times in order to measure these quantities. Waves always need variations in time and space so you need to define the space-time first.
The "oscillating thing" of light waves is called the "electromagnetic field", which is not composed of matter per se. We do not perceive it directly. We are only able to observe some of its consequences, for example the light that gets in our eye, or the heat that we feel from the sun.
A couple related questions: