My understanding is that the state of Self-Realization is a state of eternal bliss. Why in the first place one ended up having this cycle of birth and death?

Your understanding is correct that Self Realization is the state of eternal bliss. Until we reach that state we will continue to be restless. The Bhagavad Gita and other Vedantic texts help us get back to that state. They prescribe the technique of shaking off the illusion and gaining knowledge of your Self.
However, it is not possible to know why we got into this conditioned state because we are already in the illusory state. Just as a person who mistakes a rope for a snake in the dark cannot understand how he got confused. A drunk person will never understand that he is drunk.
This question will dissolve when we break free of illusion. Then you will know that the entire universe and its manifestation is just a momentary slip! Not worth thinking of. When you wake up from a dream you do not waste time analyzing the dream! You just get on with the waking state.
So the thing to do is to make a concerted effort to wake up from this delusion and get back to your original state of bliss and happiness.

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