For overnight trips
How early can I reserve a permit?
You can make a reservation no more than four months, and no less than two days, before the permit start date. For very popular sites, you may have to make a reservation at midnight mountain time, exactly four months before the start date.
If you are reserving four months before your start date, you may have to reserve each night separately. When making a reservation, please write the total number of nights you plan to use in the comments section. This way we can link your nightly reservations and only charge one permit fee.
https://www.nps.gov/cany/planyourvisit/backcountrypermits.htm