The wizard can't Ready a spell before combat begins
The wizard can cast spells during her first round, but she can't release a readied spell before her first round because she can't Ready a spell before combat begins.
As Jeremy Crawford clarified:
The options, including Ready, in the "Actions in Combat" section (PH, 192–93) are meant to be used in combat, after rolling initiative.
This isn't just an arbitrary restriction; it is a rule meant to streamline play. To see why, lets look at the first step in every combat, Surprise:
The GM determines who might be surprised. If neither side tries to be stealthy, they automatically notice each other. [...] Any character or monster that doesn’t notice a threat is surprised at the start of the encounter.
If you're surprised, you can't move or take an action on your first turn of the combat, and you can't take a reaction until that turn ends.
If the Orcs are surprised, they effectively waste their first turn and the wizard still gets to cast her fireball before the Orcs have a chance to do anything. Basically, the game simulates ambushes with the Surprise, not with Ready actions.
If the Orcs are not surprised, then you basically have a standoff that hinges (pun intended) around that door. The Wizard wants to Ready an action and so do the Orcs, but if everyone is going to ready an action for when the door opens, what's the point? Just play through the first round of combat when the door opens.
As explained in Order of Combat:
The game organizes the chaos of combat into a cycle of rounds and turns.
If you allow combats to begin with a bunch of reactions, you effectively reintroduce that chaos for no reason. For example, initiative tells you which turn occurs first, but if combat begins with reactions, whose reaction occurs first?
A readied spell and the spell slot used to cast it are wasted after 6 seconds
This isn't immediately obvious, but it's the result of several rules.
From Order of Combat:
A round represents about 6 seconds in the game world. During a round, each participant in a battle takes a turn.
you can take the Ready action on your turn, which lets you act using your reaction before the start of your next turn.
When you ready a spell, you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs.
From Spell Slots:
When a character casts a spell, he or she expends a slot of that spell's level or higher
Basically, when you Ready a spell, you cast it and expend a spell slot, but you can only release the readied spell before your next turn and the time between turns is 6 seconds.