Thanks, that worked :)
Weapon -> Create Persistent #1 (Until Destroyed / Auto Shot) -> Create Persistent #2 (1 Period Count + Initial Delay) -> Launch Missile
Marine Actor event fires the animation at #2 persistent initial.
I had to create another persistent for the added delay since the only delay options in the persistent are initial (on creation) and expires (before expiring). I needed a delay on every period.