Possibly I'm guilty of over-reading the word.
Often the question "what is the purpose of my existence?" is a proxy for some less abstract question, I think. Consider Young Frankenstein, and the gag where characters sing "Oh, sweet mystery of life at last I've found you! At last, I know the secret of it all!" because they got sex. Less cynically, it may simply be a matter of identifying comfortable values, in terms of the possible values available in the human condition in the present day. I mean you're unlikely to be honestly asking a question with a giant universal scope, if you claim that it bothers you personally.
This Destiny is in tension with Free Will (in my telling).
In retirement, my hope is to produce a lengthy, pretentious exploration of a few ideas that will doubtless help someone's insomnia.
Free Will, in this telling, exists on the logos/eros plane of the individual.
Destiny is some target on the plane out there at infinity toward which one navigates over time.
The origin of this coordinate system is the heart, and one may or may not hold a connection to the Creator via the thymos.
Otherwise, it's just so many chemical reactions.