Thank you for this question Menas! I had to ponder it for a while.
I would say that life, aliveness, is one of the primary properties of not the universe, but of consciousness, because to me, the universe is the same as consciousness. So yes, aliveness is a primary property of … everything. Consciousness is alive and aware. I see no randomness, but neither do I see purpose in the way it is usually understood, as an intellectual goal. The purpose I see could maybe be called joy, beauty, truth, self-experience, and it is not a goal to be attained in some future, but a state of inspiration, like the outpouring of a fountain.
Would love to read other perspectives on this 🙂