Well, to be clear the 0-level events would only be one session, maybe one and a half. They wouldn't (at that point) be capable of any spellcasting, armour wearing, etc...
I know it realistically takes more than, say, one week of training to become a level one fighter, but if you read any of the classic-style coming of age fantasy stories, the fighter-types learn to fight when they have no choice. Mages find a few simple spells written in a book ,and they expand their knowledge from there...
Here's a rough outline of the campaign start as I see it:
The first session is all about the standard small town (500 people or so) life. A spring festival is upcoming and the young people of the town (including 3 of the 5 characters) are all helping prepare. They are aware of each other but do not know each other personally. Of course, this is the age when daughters are looking for husbands, and sons are noticing them, so the characters mingle a bit. A week or two before the festival, a small caravan of people (including the other 2 players) arrives from a fairly distant, much smaller village looking somewhat travel weary. Something is moving in the woods, there is a rumour of coming war, and they are fleeing for safety.
The inhabitants of this distant village are not often seen in this town, and the locals tend to think them and their customs odd. In fact, both PCs from this village are Psionic, so it gives them a little mystique that should fit well with their classes.
The level 0 characters are involved in a simple search party/patrol at this point while the mayor tries to assess any real threat to the town. They might have one simple encounter here, a lightly armed goblin scout or two. I would most likely have them traveling with a town militia man, War1 or War2.
At this point the town is aware that there is a real threat. They move into a defensive mode, and the young villagers are clearing woods, digging out rusted weapons, helping the blacksmith, the fletcher, etc...
They gain their first level here. Fighter-wannabes are working with the blacksmith and learn to sharpen a sword, fit armour, and in the process they hear some tales of when the blacksmith was in the Royal Guard twenty-odd years ago. He shows them how the handle a sword and use a shield, how to don armour etc...
The two Psionic characters are a little harder since they don't need 'training' to be Psionic. I was thinking that they both knew that they were 'special' but needed a jolt, either physically or from the stress of the goblin ambush, to awaken their inner voices.
Other characters could learn from the fletcher (Rangers and Barbarians), tavernkeeper (Bards and Rogues), apothecary (Wizards and Sorcerors), or clergy (Clerics and Druids).
The character is now level 1, and they can embark on their first real adventures. They can continue to train with their local masters until at around level 3 or 4, when I envision the town being overrun, and the townsfolk slain except for the few youngsters that are returning to the town from another quest.
At the end of this introduction, we should have a nicely tied together background, a common foe, and more than enough reason for the PCs to strike out on their own.