You are falling into dualism's a priori logical quandary, as it assumes there was a 'first' cause, a beginning, a start. Second, your question is not logical, as to say that existence 'comes out of' non-existence is to say that the first cause is from that where there are no causes. Third, if it had a 'beginning' then logically it would have to have an end; all of existence would have to end in non-existence as to have a beginning is to be non-eternal. And fourth, when non-existence is spoken of, you really mean the sensual universe as perceived, and not material existence, as to a rock or a stone which has no perception, no rudimentary senses, no consciousness, there is no difference between non-existence and existence.
Plotinus writes at the start of the Third Ennead: Second Tractate in The Six Enneads:
To make the existence and coherent structure of this Universe depend upon automatic activity and upon chance is against all good sense.
Such a notion could be entertained only where there is neither intelligence nor even ordinary perception; and reason enough to be urged against it, though none is really necessary.
Eastern philosophers, both Buddhist and Hindu (Vedanta) assert that there never was a time when there was no existence. The universe goes through cycles of expansion and contraction; but time's arrow goes eternally in both directions, there was an infinite time before us, and there will be an infinite times after us. The real question is perception.
Nagarjuna writes in his Malamahyamakakarika (The Fundamental Wisdom of the Middle Way), Chapter XXIII, Examination of Errors, (Jay Garfield translator):
That by means of which there is grasping, and the grasping,
And the grasper, and all that is grasped,
All are being relieved,
It follows that there is no grasping.
If there is no grasping,
Whether erroneous or otherwise,
Who will come to be in error?
Error does not develop
In one who is in error.
Error does not develop in one who is not in error.
Error does not develop
In one in whom error is arising.
In whom does error develop?
Examine this on your own!
Buddhists affirm dependent origination, Advaita Vedantists affirm Maya. Both affirm that in order to negate being, you must affirm being. To affirm both terms, is to negate both. Both negate being and non-being. Again, Nagarjuna says (Chapter XXVII):
If it could be established that
It is both finite and infinite,
Then it could be established that
It is neither finite nor infinite
So, because all entities are empty
Which views of permanence, etc., would occur
And to whom, when, why, and about what
Would they occur at all?