My solution is to be very, very tired which isn’t a problem when backpacking. A few years ago, I car camped for a couple of nights in the Sierra Nevada to acclimate and I wasn’t tired. Had a lot of trouble sleeping partly due to the sounds. Seems like there’s more noise in an area with more people like a car campground. In the wilderness, I find things more peaceful.
On the PCT, the night before getting to the famous McDonald’s at Cajon Pass, I stealth camped at a highway picnic area and didn’t want to put up my shelter. I could have sworn that snakes were everywhere around me as I lay down to sleep in a place sheltered from view by some brush. But it was after a 25 mile day. The next thing I knew it was morning and ten miles to McDonald’s.