I thought it took a few hours to fluff up. I once had to assist a chick out of their egg. And it didn’t fluff up for a few hours.
So here’s the assist story. A hen was broody. Started to throw eggs off it’s hidden nest up above in shelves in my storage trailer. My husband heard chirping and looked everywhere and didn’t find a chick. He saw an egg on the floor a bit cracked and just tossed it outside thinking it was a dud. We went back later and it was starting to get covered in ants. It was a live chick! We had to crack the egg and get all the ants out. It survived. Unfortunately the heat got it along with 4 of its siblings a week later (but before then it was strong and healthy). So sad, because I was the first anything it saw and thought we had a bond.
No, it’s wet because it was in an egg. They’ll dry up in the heat lamp. Put it in the brood you’ll be keeping your hatched chicks in and place it under the heat lamp. No need to rinse it off. It’s normal wetness. Won’t hurt it.