Is every soul bound to be liberated eventually? Does the timing depend on the soul, or divine intervention?
No, its not the destiny it is the necessity of every soul. Without knowing who we are or the self before death arrives is like living a dream. And in a dream we never know we are in a dream first, and where we will wake up after the dream second.
Calling enlightenment destiny creates an illusionary thought, that it will happen automatically, eventually since its a destiny, destiny means it will happen for sure. But it is not like that, to attain enlightenment one has to seek it, practice it.
every human has two options, to live the life with nature like any other animals do OR to rise above the nature, this possibility is true for humans only. So, its not a matter of time its a matter of doing it.
After enlightenment you will know, you are in a dream, and where will you wake up, what else is needed in this life? You know everything then.