It might be little bit too late, but I would like to write my interpretation.
and I could not find where to write the answer for this, I left the comment here to answer for it.
It mean "My dream, the universe" or "The universe I dream of"
because the universe is not human and won't dream anything. so it is "I (私)" who dream of.
probably it will help to understand when adding 私が to 夢見る宇宙 so it will be (私が) 夢見る宇宙.
sometime the subject is omitted from a sentence when it is so obvious.