So using machine learning and optimization techniques in general to solve inverse problems, so your input is something meaningful, is a way to unlock SDF rendering without requiring a reinvention of the whole tool universe.
If someone wants a modest-scope project, it would be applying these kinds of techniques to blurred rounded rectangle rendering[1]. There, I got the math pretty close, fiddling with it by hand, but I strongly suspect it would be possible to get even closer, using real optimization techniques.
[1] https://raphlinus.github.io/graphics/2020/04/21/blurred-roun...