I think whether or not something will change its souns after burn-in depends on its physical property.
But I am not an expert on device physics.
Tubes don't have moving parts, but since the filaments kind of burn away and the plates get bombarded by electrons, they actually wear out gradually. I would not be too shocked if their sonics can gradually change after initial burn-in or even long use.
Othe other hand, metal conducts electicity by having delocalized electrons in the conduction band (apology for these lingo I picked up in quantum classes), and I can't imagine electrons flowing through cables would change any property of the material.
Solid state device such as BJT has p-n-p sort of structures. I vaguely recall from my electronics classes a small amount of charges have to first flow across some junctions to make the device work. But these should happen very quickly with regular use. When I first bought my SACD player, the headphone jack could only drive my headphone to barely audible volume. After a few hours of listening the volume gradually got to pretty loud. The volume difference was very big and could not be mistaken. I guess it may be a sign of burn-in.
My recent experience with class T amplifier shows that it gradually sounds smoother within the first 24 h of use, and then stops changing. In this case, it may be my brain adjusting to the sound or just placebo effect. I am not so sure if this is really a valid observation.
So my personal understanding and experience is that SS electronics need very little, if any, burn-in.