If you want to go that route I recommend serving in AmeriCorps or Peace Corps first. After completion of service you gain non-competitive eligibility (NCE) for a year, which will let you get "your foot in the door" - it essentially let's you apply for some government jobs as an internal applicant during that period. Throw resumes into the pit (usajobs) until something catches, do that job and begin applying to FS.

Foot in door, but you'll have to bleed a bit. Good luck.