It is a much different read if you approach it with some prior knowledge of what it was intended to be. The preface plainly states that Milton wants to "justify the ways of god to men."

The plot and structure are a direct knock-off of Homer's epic poems. Milton followed a regimen of writing that was old before he was born, in that first people would write lyrics and sonnets and then eventually hone their skills toward writing an epic. So there's not a whole lot of meat, for lack of a better word, in the structure of the poem itself. It is assumed that the reader knows their classics and identifies the references themselves.

The clever parts are in the details. Milton's angels and demons have philosophical/political debates and conversations which invite the reader to consider hard questions and make conclusions of their own. Milton even considers the mathematical and philosophical questions of being in the poem, for example. Satan asks permission of the "throne of Chaos" to travel through his domain from Hell to Earth. Satan's plea to Chaos is that by creating his universe, god stole from him and he should help anyone who opposes that creation. So it is implied that Chaos is a force perhaps not comparable in status to the one god, but certainly above immortal beings like angels and demons, so perhaps Chaos and God are naturally opposed, entropy vs order, etc. And even this is ideologically and theologically consistent down to the detail. Satan doesn't really know how powerful Chaos is, but should he? Chaos is older and greater than any angel or demon, so it follows that angels and demons would not know exactly how powerful Chaos is, but would know that Chaos is greater than they are. Similarly, the battle scene in heaven between Satan's rebelling army and the angels loyal to God begins with all of them not really knowing whether they can be killed or not. They consider whether all of their fighting is for nothing, because they're immortal. This is another thing that, logically and philosophically, they would not know on their own because they didn't create themselves, after all. They were created, and thus are necessarily lesser than the creator who does know.

"Justify the ways of god to men" to Milton was an attempt to "fix" Christian doctrine, to fill in the blanks and missing parts and make it all fit together without any contradictions or failures of reason.

But here lie conclusions that are difficult to reason away: if Satan rebelled against God and God is all-knowing, why didn't God stop him? Is all of creation an experiment in free will (which makes everyone a pawn), or can God himself not kill one of his immortal angels? If the latter, is he not really God if there's something he cannot do? Was Jesus/The Son just a ruse to root out disloyalty among angels?

And really all of these things get to "does the universe even matter or does whatever created it not care about it?"

The whole thing is not just a religious text, although it is about a religious doctrine. It's a text meant to teach people how to think, so that they would overthrow their kings and noble rulers and rule themselves, just as Milton portrayed in his last writing (a rewrite of the story of Samson Agonistes).