There is no set time that a government hiring process takes. The organization has an incentive to speed up the process and get someone in the vacant position as soon as possible, but it also has an incentive to be thorough which can slow down the process.
If you are screened out of the selection process when the organization’s human resources department reviews all applications for the minimum requirements, it may only be a week or two after the closing date that you receive your rejection letter, lick your wounds and move on.
The longer you have to wait on hearing back, the better, but there is a limit. If you don’t hear back after a month, you can most likely forget about that job. Do not delete electronic copies of the application materials you sent because there is still a chance you’re in the running, but don’t hold your breath. The organization may be interviewing other candidates and will notify all applicants that they were not selected after they choose their new hire.
If you are selected as a finalist, you should hear back in about two or three weeks to set up an interview. After you interview, you should hear back on the final selection within a week or two.