Yeah, there's still room to join.

If you're going to play a military character, I would personally recommend starting at Griffith Park or Pasadena, as the military would try to fortify the former at Griffith Observatory as the elevated terrain there would allow them to look over the epicenter of the outbreak around Downtown LA and East LA, and the latter would provide a vital chokepoint for the military to control the outbreak between the various valleys in the LA area. However, you can start at LAX if you wish.

The military at LAX under General Matthias has by far run a police state there, but it might be interesting for a military character to be a good guy instead of following orders to do bad shit to people.