Pull the National Weather Service forecast for your destination and see when you should lock in a site.
Shoulder season — 1–2 months is enough
Spring and fall are the easiest times to find a spot. Weekdays are almost always open, and weekends usually book 1–2 months out except for holiday weeks (Memorial Day, July 4th, Labor Day). This is the best window to try a popular park without a six-month wait.