Theory but I think the ins colonized hell and more to the point turned it into Hell. As in, the imps aren't spiritual beings, nor are the hellhounds or even Stolis and his people.
Basically, I think that pre Sins Hell was just like, another dimension that living beings existed in. Then the Sins rocked up/got booted out of Heaven and turned it into an afterlife and bumped Solis's family and others like them from top dogs to lesser lords and their subjects even lower.
Yeah, I've thought about that possibility a fair bit myself, and while it's definitely possible, I feel like it doesn't quite fit.
For one, I'm not sure if the story would full-on vilify the Sins like that, framing them as colonizers who conquered Hell and subjugated its people. As it sort of distracts from what I imagine is both Helluva's and Hazbin's ultimate point of Heaven being the true final antagonist of the franchise.
More substantially, the idea of Hell simply being some random 'alternate dimension' feels a bit underwhelming when it seems more that there is SOME kind of connection between Heaven, Hell and Earth. Personally, I think it's more likely that Hell has always been treated as a 'dumping ground' by Heaven for all their 'trash' they don't want to look at anymore. Like perhaps Demons are some failed or rejected proto-version of humanity. Maybe Hell itself is some kind of failed version of Earth.
From what we've seen so far, I feel like it makes sense that it would turn out that everything in Hell, from its people to the Sins to the humans trapped there to perhaps even the world itself all represent the 'trash' that Heaven wanted to get rid of.