It's complicated and some of it is up to the DM
Let's start with the Surprise rules:
The DM determines who might be surprised. If neither side tries to be stealthy, they automatically notice each other. Otherwise, the DM compares the Dexterity (Stealth) checks of anyone hiding with the passive Wisdom (Perception) score of each creature on the opposing side. 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. A member of a group can be surprised even if the other members aren't.
A lot of this initial work is determined by the DM, and only they can ultimately decide who is surprised, who isn't, and when it's time to roll initiative. But ultimately, if you're all in actionable points, then it's time to roll initiative and figure out surprise.
But let's look at your scenario.
You've got several groups of players:
- The Party
- The Orcs sitting around a campfire
- The orcs in a tent
At this point, the Wizard wants to cast invisibility and move to the Orcs. This is also the first point the DM has to determine whether or not we're talking about combat and the need to track initiative.
If the party is far enough away from the Orcs and never got close enough to be noticed, then they can rule that the spell can be cast, and that they are far enough away that the Verbal component isn't an issue for being noticed.
But a DM could also rule that if they're close enough to have found the Orcs and scoped out the situation, then they are also close enough to be noticed and that it's time to roll initiative.
But let's say the DM wants to allow the casting and have the wizard approach invisible.
The wizard approaches
Being invisible doesn't make you undetectable. The Wizard will still need to roll stealth and then the Orcs will have their passive perception scores determine if they notice the Wizard approaching (sound, ground disturbance, etc.)
Again, the DM could ask for initiative so that the time and actions can be better tracked, but it's also reasonable to let this play out. It's the DM's call.
If the players attempting to be within range of attacking (whatever their movement speed is), then the DM again could ask for initiative rolls or simply ask for the party to roll their stealth to see if they can get that close. Otherwise, the DM determines how far off they can be without fear of being noticed and has the party at that distance.
Wizard wants to get close enough for a thunderwave
Here is the moment the DM really must roll initiative and make the determination of who is surprised and which creatures are currently involved in combat.
It is possible that the Orcs are ahead in initiative and end up losing their Surprised state before the Wizard has a chance to cast thunderwave.
It is important to note that once thunderwave is cast, the Wizard will also lose their invisibility. If the Wizard's initiative is after any of the Orc's they are currently in melee range, then those Orcs would have an opportunity attack if the Wizard leaves because their turn has ended and they can again take reactions.
Any creatures not directly in combat then roll in initiative
At this point, the DM can also determine when any remaining creatures (the Orcs in the tent, the party if they were far enough away, etc.) roll initiative and join the combat.