Tips on becoming a DOD Civilian

I am currently a Budgeting Analyst, I have my Associates degree and plan to continue on for my Bachelor's. I will be medically retiring soon and my #1 goal is to continue my civil service and become a DOD Civilian; however that's seems to be almost impossible without connections. I absolutely LOVE my job in the Army and appreciate the military environment and am hoping to continue serving my country as a civilian. If anyone has any tips or advise I would graciously appreciate it. Thank you!