This question is mainly based on this previous question.
Quoting from Admiral Ackbar from the linked question (emphasis mine):
While the planet in question may at present be deliberately underdefended, the instant we move forces out of hiding and in its direction, the First Order will realize that we know the location of the weapon. They will mobilize everything in the vicinity to protect it. Their fleet is too large for us to fight our way through.
So knowing that:
Starkiller Base just crippled the New Republic with a giant, red beam of destruction that could not have failed to give away the position and the destructive power of their superweapon. Furthermore, the First Order must have known that before they fired the super weapon.
Why didn’t the First Order mobilize their fleet to protect the base right as they destroyed the Hosnian system?
- It seemed like their plan all along was to defend Starkiller Base with a large fleet.
- It makes complete tactical sense to defend the base so that it isn't immediately destroyed after you use it.
- More so when you consider the first Death Star, which was destroyed by a bunch of rebel starfighters because you only defended your superweapon with a bunch of TIE Fighters.
- If they mobilized the fleet beforehand, they might have tipped off the New Republic. But they could have called in reinforcements the moment they fired the weapon at which point it would have been too late for the New Republic to evacuate. Maybe this is a reason?