Hi Chris R
I would definitely set the hog house in place now. Some hogs will move in fairly quickly but others need it to become part of the landscape first, so the sooner the better. Most hogs like to furnish their houses, themselves, so I would just put a very small amount of dry leaves, grasses, etc. in to give them the idea and then leave piles of suitable bedding nearby. Then a hog can choose what is wants and take it in itself.
Don’t be surprised if they still choose to nest under your shed! But they may use the (I’m guessing you mean one of the ones called hogilos) home later on. It can sometimes take a couple of years and they may use it for naps between snacks or as a day nest in the Summer. All useful for hogs.
If it is a hogilo, I would peg it down, so that predators can’t tip it up. I have one, which is wedged under a shrub at the back and fixed with a piece of wire over the arch and pegged down using tent peg type fixings.
Good luck with all the hogs. Hope you get a resident in the house.
