In many places you will read that just after the big bang, the universe was filled with very hot gas which appeared to be in thermal equilibrium. You will then read that this is actually quite a low entropy state, due to gravity. Though all the matter particles and radiation are in thermal equilibrium, the spacetime where they live is unusually flat. A state of much higher entropy would be to have things clumped together in complicated ways, with a bunch of large black holes hanging around.
Fast forward several billion years, and we get to today, where the sun is shining, allowing us Earth lifeforms to exist. This works because space is cold, while the sun is hot, so we can live off the temperature difference. If we ask why the sun is hot, we find that it's hot because it's fusing hydrogen into helium.
So I know the beginning of the story and the end of the story, but not the middle. How do we get from "spacetime is unusually flat" to "there are hydrogen atoms around that you can fuse into helium"? In particular, how does gravity make a difference: if $G$ was 0, would all the nuclei in universe already be helium (or I guess iron)?
EDIT: To clarify the question consider the following two scenarios:
The "no fusion" universe: In this universe, nuclear fusion is impossible. Stars still form due to gravity and they still get hot as they collapse, but they don't shine for nearly as long, since there are no fusion reactions happening in the core to replace the energy lost to radiation. Stars rapidly become white dwarfs without passing through a fusion stage. This example makes it seem like nuclear physics is somehow important to answering this question.
The $G=0$ universe: This universe has no force of gravity, it's spatially uniform. We can still allow it to expand like our own universe, but I guess it wouldn't be due to dark energy or anything, that would just be the shape that spacetime happens to have. After 13 billion years, I'm guessing this universe would be uniformly full of cold hydrogen gas? Though the lack of gravity definitely rules out the existence of stars, it seems like an alien civilization that travelled to this universe could sustain themselves by collecting hydrogen gas and building fusion reactors. If an alien civilization could live there, then entropy must not be at a maximum yet. This example makes it seem like gravity is almost irrelevant to the issue, though I don't think that can actually be right.