Is every soul bound to be liberated eventually? Does the timing depend on the soul, or divine intervention?
For evil persons Their destination is andhamas that is their true aspect or attribute. The whole creation is meant to realize once true state. From BG. 16.19-20 Its clear that moksha is not for evil persons.
तानहं द्विषत: क्रूरान्संसारेषु नराधमान् | क्षिपाम्यजस्रमशुभानासुरीष्वेव योनिषु || 19|| आसुरीं योनिमापन्ना मूढा जन्मनि जन्मनि | मामप्राप्यैव कौन्तेय ततो यान्त्यधमां गतिम् || 20||
tān ahaṁ dviṣhataḥ krūrān sansāreṣhu narādhamān kṣhipāmy ajasram aśhubhān āsurīṣhv eva yoniṣhu āsurīṁ yonim āpannā mūḍhā janmani janmani mām aprāpyaiva kaunteya tato yānty adhamāṁ gatim
BG 16.19-20: These cruel and hateful persons, the vile and vicious of humankind, I constantly hurl into the wombs of those with similar demoniac natures in the cycle of rebirth in the material world. These ignorant souls take birth again and again in demoniac wombs. Failing to reach me, O Arjun, they gradually sink to the most abominable type of existence.
The answer to this question depends on how one interprets the following Gita verses.
These vicious men, oppressive, cruel and sinful as they are, -- are always hurled by Me into demoniac wombs in life after life, in the transmigratory cycle.
O son of Kunti! Falling into demoniac wombs, in life after life, they go to still lower states of degradation, without attaining Me.
On the basis of such texts, some schools of Vedanta like those of Sri Madhva and Sri Vallabha have propounded the theory of taratamya or inherent qualitative differences in Jivas, some being made for salvation and others for degradation. There is no eternal damnation in Hinduism, but this confinement to 'adhamam gatim' or continued embodiments among the lowest creatures like insects, fish, snakes etc,. corresponds to it as the wages for confirmed evil doers.
There is a theoretical possibility of salvation even for such degraded souls when Divine grace descends on them through Incarnations and through very holy saints. Since Samsara or the transmigratory cycle is a never-ending process, perpetual involvement in it is the attaining to that most heinous destiny - yant yadhamam gatim.
Srimad Bhagavad Gita commentary of Gita 16.19-20 by Swami Tapasyananda
Most other sects do not interpret these Gita texts so literally and say that everyone would get liberation, some early and some very late.
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.