Presuming first that we are communicating as to "universe" meaning "the all" and not just "our universe" then I'd go back to the very first part of your first post.
Essentially, it argues that the universe could not be eternal, since this would require an infinite past.
I doubt Epicurus would go much past that without stating that "the universe / the all" must be eternal, because it is inconceivable that there was ever a time in which "the all" did not exist. It certainly appear to us that the we exist, and that it makes no sense to consider that there was ever a time that the all did not exist, so I would rule out of hand any supposition (it would require an infinite number of steps to get here and that's not possible) that conflicts with what all appearances tells us does exist.
I'm sure someone here can probably do better than that for an answer but any fundamental logical paradox like that has to be resolved in the end by relying on the apparences (sensations) which in the end are all we have as contact with reality. The mind can image all sorts of constructions that defy reality, but devotion to what nature has given us is why in the end we go with sensations and not with pure logic that ultimately cannot be reconciled with the senses.