Chickens are afraid of everything.
I shove a new bag of feed or pine shavings in the coop and chickens explode out of it like something is trying to eat them. Scrape out some dirty pine shavings and something is wrong. Add new pine shavings and it's like little kids playing don't touch the floor. The pine shavings might melt their feet. Add a different colored feeder and they won't get within 5' of it.
Stick the hay in, wait to see if they get over it, if not stick the chickens in when it starts to get dark, and lock the door. By the time you let them out the next day they'll probably be over it. I empty the coop and stack the bags of new bedding in there then wait for a day of bad weather when I plan to lock them in. Then dump all the bags while chickens squawk and hide on the roosts. By the time they get let out the next day they've had no choice but to walk on the shavings and then they have no problem going back in before dark so I don't have to shove silly chickens in that evening.
One thing to keep in mind though is that hay isn't actually a good bedding. Neither is straw. They do not absorb moisture. In fact they insulate moisture as well as they do heat. Your coop will be wetter with hay or straw than it will be with no bedding. That leads to smell, mold, and illness. You can add hay to the nest boxes and you can add hay in the winter to help insulate but make sure there is a good absorbent layer under it. When I laid down straw last fall for the winter I put a layer of pine pellets which are about as absorbent as you can get, several inches of shavings, and then the bale of straw. I still cleaned out some gooey spots the next spring and when I started stripping the coop I found all the pine pellets had completely broken down from the amount of moisture that had been held under the bedding. My coop is 170sq ft but I only clean it out twice a year because it stays dry and without smell. Using hay or straw by itself I'd probably have to strip it out every couple weeks except the coldest part of winter and then leave it to dry for a day if I didn't want to be knocked out by the smell when I stood in the doorway and end up with sick chickens. I would never use it in summer. That would just be a mess. I hated putting hay or straw down in foaling stalls when we had pregnant mares because it meant I'd have to nearly strip the stall daily until they foaled and the foal was dry enough to not have all the shavings stick to it. If I didn't empty it daily every area they peed would remain wet even with shavings under it and the ammonia would build until by the time they did foal the level at the bottom of the stall was enough to cause respiratory damage in the foal. With pine pellets they may cost a lot in the first place but by the end of the season I've saved money because I don't even have to remove the wet spots. I just remove the manure and stir the wet spots into the rest of the horse stalls for the pellets to absorb and break down into more fluffy bedding. I barely remove any bedding all winter from my horse stalls and only have to add a couple bags once to each stall before spring. Then again when everything thaws in the spring and there's tons of humidity in the air.
Also your chickens will eat hay or straw. A dozen of my japanese bantams (very small chickens) can eat 3 bales of straw in a few months over the winter. First that means your hay or straw will disappear much quicker than shavings, good news is you won't have to scoop it out then, and you'll suddenly find your coop bare (I was surprised to find mine only had shavings again after a month when I'd laid down 2 bales of straw) and second if they don't eat it all quickly or you don't empty it frequently they'll be eating wet, =moldy, hay which again means illness and possibly death before you even realize what happened.
They immediately flew out of the coop. Then I tried to put them back in one at a time (after gently talking to them and holding them). I'd set them each in the nest or near the hay while touching them to show them it was okay, but I still got the same reaction.
