You can do anything you want. Look into state and federal jobs. Understand timing is everything with goverment jobs. The (USAjobs) jobs are posted for certain future dates for intervierws then future dates of placement. My son started applying about six months from his end date with the Army. He got contacted by 4 different Homeland Law Enforcement departments over the course of the first three months for interviews. The job he accepted wanted him before his six months was up. Then he contacted the other 3 agencies to stop the progress on his application with them. He also contacted the NJ Guard which accepted him. The Guard allowed him to leave the Army a little earlier than his end date. But he had to commit 4 years with the Guard. He loves his new job. The Guard has also been enjoyable. He commands a company in the Guard whose battle streamers include Monmouth, Yorktown, Antietnam, Gettysburg, Meuse-Argonne and Normandy.
When he graduated college he had 3 days from graduation to report to Benning. This time he only had one day from the Army to start his new job. He then left for six months of training with the agency.
The grass may seem greener but be careful, timing is very difficult. If you have a wife and kids in tow it can be very stressful with the application process. Accepting employment at some agencies may mean you will live and work where they decide much later on. You really must think hard on this decision.