The question 'why does something exist' is arbitrary related to the other question: 'why does nothing exist?'.
The universe is infinite, and transcendental. Transcendentalism is the idea that all categories and order dissolves as they're related to infinite. A rationalist says, categorically, nothing is nothing; and something is something. A transcendentalist, however, asserts nothing is something; and something is nothing. The two are dependent; the two are one.
The universe, across infinite, is paradoxical. Thus, to a transcendentalist, we both exist and do not exist. Existence is permeated by uncertainty, and the prospect of nothing.
TO put it another way, undifferentiated infinite, being in a state of voidness (nothing), contains the latent potential for all manifestation.
To put it another way, why should infinite differentiate into finite parts? Why should order exist? Why should it emerge out of chaos? It's paradoxical, but then ask why should chaos exist? Why shouldn't there be life, and order?
It is self-evident that both exist. We both exist, and do not exist; in the sense all existence is, in part, an illusion.
I believe that in the state of absolute nothingness, the prospect of something remains transcendentally entangled; nothing and something are inseparable. You cannot have nothing without something.
This entanglement instills in nothingness an infinite imaginative potential; an unseeable observer bias; a freedom of manifestation; a consciousness of the something beyond; in the same way, throughout our existence, there is an unending presence of uncertainty. I think, by many, this is identified as 'God'. It is the void we were born out of and return to.