Recall the distinction between the singular world vs. the various possible ways a world could be. (The latter are misleadingly called "possible worlds", but are better understood as world-states, or maximal properties.) We may think of the universe as a "lump", and the actualized possible world as the maximal "property" instantiated by the lump. But note that in general, it isn't the case that every object could instantiate any property. The entity that I am, for instance, is essentially human, and so couldn't instantiate the property of being a poached egg. (If an evil wizard transformed me into a poached egg, then the resulting object wouldn't be me any more.) This then raises the question of whether the world-lump has any essential properties, or whether it could actualize any possible world-state whatsoever whilst retaining its identity. Put in more intuitive terms, we can ask: could our world have turned out in any possible way? Or are some possibilities so extreme that they could only be realized by a different underlying universe?
I'm inclined towards anti-essentialism here. It seems tidiest to say that each possible world-state is a way our world could have been. But to explore the alternative, I think the most likely candidates for essential world-properties would be the laws of nature. We would then say that our world could have turned out in any nomologically possible way. It remains true that there could have been different laws of nature, but not in our universe. A change so radical would disrupt its very identity, and turn it into a different universe. (Just like turning me into a poached egg. The radically different properties can be realized, but only by a different entity.)
One might also want to build in the "initial conditions" of the universe as being part of its essential nature. Then, if the laws are deterministic, we would reach the conclusion that our world couldn't have turned out differently at all. (Again, things could have turned out differently. But that would be because a totally different universe existed in place of ours.) If indeterminism is true, at least a few more possibilities are opened up for us. But they will still be extremely limited compared to what philosophers usually take to be possible ways our world could have been.
This narrow account of local possibility might line up with pessimistic accounts of primitive modality. It doesn't settle those broader questions though. We are still left wondering whether, say, another universe with different laws really could have existed in place of ours. (This lack of progress is unsurprising, though, since I'm inclined towards a deflationary understanding of de re modality and debates about essentialism as merely terminological. There are no deep facts about my not possibly being a poached egg. All this really means is that of any entity that was a poached egg, we would refuse to hold it in the extension (or intension) of 'Richard Chappell'. Haeccaeities or identity facts are not fundamental aspects of modal reality. But that's a post for another day.)
But for those who take essentialism more seriously, do you think anything is essential to our world-lump?