There are a few ways you can handle it. Sure, you can retroactively assign a backstory to the poor lad who was working as a pigfarmer while studying magic by candlelight at night. Also, don't lose sight of the fact that you pretty much know if a character is destined to become a wizard when he level's up when you roll their stats, so you would typically know at that time. In other words, this isn't something you suddenly realized when the character reaches 10 xp's. The stories can be created when the characters are rolled up if you have the time and inclination.
Another alternative, and one that I prefer, is to put in a long period of downtime in the game after the conclusion of the first adventure. You could even insert this time in the middle of a gaming session if it's convenient to do so. The story can be that after this adventure, all the characters spend several months or even years assimilating their experience into the level advancement benefits. This dimension of realism doesn't just make sense for wizards, either. At least with the wizard character I can say that they suddenly had a eureka moment and now they have figured out how to unlock the magic in these formulae that they've known for some time now. With a warrior, it's much harder to justify how they suddenly went from some average joe to a competent martial artist, or similarly with a thief character who suddenly becomes adept at several skills that would normally take a very long time to gain proficiency in.
Thanks for the comments. In our current game we took nearly a year off between level zero and level one for these sorts of reasons. I'm likely to be running a DCC game in the future and I've been struggling to make sense of this facet of the rules as written. I wondered if I'd got them muddled.
I won't have the year off option available, but have been mulling some other ideas. At least I didn't just misunderstand. Cheers.