It's more crowded than it used to be (I've heard). We went that week our first trip there in 2009. Very low crowds. It was unseasonably hot that year though, so prepare for that. It topped 100 several days. Looking at more recent crowd levels, it's definitely more crowded than it used to be.
2010 from TP: First week ranged from 1 to 4, with the average being 2.
2017 from TP: First week ranged from 4 to 8, with the average being 5.7.