Basically, that's the question behind the so-called 'string theory', which aims to derive the value of physical constants such as the velocity of light in vacuum from topological considerations over the structure of space-time.

No luck yet, but this attempt, among others, has certainly kept many scientific and mathematical minds busy in the past 40 years !

I know very little of string theory other than it seems to have fallen a little out of fashion recently, and I did not know that one of the reason it exists is as you succinctly describe its aims: very interesting. I work on and off with biochemist Rupert Sheldrake on a mechanisms for memory, albeit I use top down principles of quantum entanglement to show how information might be transferred across time. He uses observation and what he describes as a system morphic resonance, the conclusions of which are remarkably similar to my thesis.

I mention this because in his book 'The Science Delusion' (2012) he examines the role of fundamental constants including light speed to discus whether the laws of nature are fixed or whether they are possibly evolving. And then there are a few other physicists working on variable light speed, and even a few astronomers, but with what results I have not recently heard much.

I have always thought that perhaps we do not question the apparent constancy of light speed in a vacuum nearly enough, and this is probably closely connected with why we know so little about gravitation other than its effects.