The initial wave will include just a few thousand initial invites. As the closed beta continues, the number of players invited will increase in "chronological order of when they signed up." If you still need or want to sign up, you can do so at the PS2 on PS4 sign up page at the PlanetSide 2 website.
The full game is expected to be released later this year. There is also no word yet on just how long this closed beta period will run for.