This beginning does not grip me. Indeed it puts me off. For three reasons: I've had quite enough of books beginning with some dystopian teenage initiation rite. The claim that "this is the day" is completely vague and unexciting. And after the third unfamiliar concept (Booster, Emergence, Divide, Purgatory) I'm completely bored and ready to close the book.
We can't do anything about the first problem. If that is what your story is about, then that's your story. There will be readers who are waiting for the next Hunger Games. But I'd not put this so blatantly on the first page and rather emphasize what differentiates your story from its famous and bestselling predecessors. You don't want to sound like a rip-off.
As for the second problem, your are breaking the show-don't-tell rule. You claim that this is a special day, you even give it a name and report that everybody is afraid of it, but that is not making me afraid. What you need to do, and in the very first sentence, is create an emotion in the reader. If you write genre fiction, the first sentence needs to be the best in your book. I'll come to an easy solution after talking about the third problem.
When I read fiction I don't want to learn vocabulary. There are quite a few successful books out there that are written in some imaginary future English and spill over with foreign terms. There are also many books that feature more characters than a teacher has pupils to learn the names of in his life time. I don't like this type of book, but some obviously do. If you want to grip me, you'll have to be very careful and introduce foreign words slowly and with some kind of mnemonic device for me to remember it by. For example, if there is a Booster, introduce its name when you show what it does. I'll certainly remember what happens, and I'll memorize the name alongside the event. Or, and now we come to the example of the good first sentence, you could give names that are at least partially self-explanatory, like Sector.
When you write about Sectors C and D, I don't exaclty know what delimits those sectors, but since people live there (see how you name the object while showing what happens there?) and since the word sector means something that is closed off, I have an image of some kind of city block that is separated from other such city blocks by some technical means or guards and for some reason that I am curious to learn (see how you evoke an emotion in me?).
What I would do with your snippet of text is delete the first three paragraphs completely and start with the fourth. "A lot of people think that Sector C is a horrible place to grow up in." That makes for a great, gripping first sentence. It makes me curious. Why is it thought to be a horrible place to grow up in? And (see above) why are these people living in sectors instead of towns? Where are we and what kind of world is this? I actually want to read that book and learn more! And the second sentence is great, also. Why is it actually okay to grow up in Sector C if everybody thinks it's horrible? Thieves? Interesting. Used to it? Even more interesting. Now I want to learn about that person, what kind of person he is and how he lives.
It is a common experience that the first part of your first draft is usually rubbish and that you can just delete it completely. Don't rewrite it or work on it, just throw it away. Not the content, of course, you can (and might need to) tell everything about boosting and stuff in the course of your book, but get rid of the warming up that you needed to write to get into your text. These first three paragraphs are like a sportsperson jogging and stretching before they attempt to jump 7 meters. Necessary, but not what we came to see (well, except for those voyeurs on YouTube posting closeups of athlete's asses, but you can satisfy your voyeurs on your writer's blog).
Note, how I assumed the narrator is a boy. I'm not sure what made me think so. Maybe because I'm male I project a male perspective in non-specified characters. Maybe because "he" has a sister, and I'm sort of balancing this. Anyway, make sure that you let readers know right away what gender this person is, but in a natural way. It could be stated in the blurb. Or you could do something like "... horrible to grow up for a girl", though I wouldn't tamper with the first sentence. Make it clear somewhere in the first paragraph.
Finally, somehow the term "Emergence" reminded me of Veronica Roth's Divergent trilogy (with the titles Divergent, Insurgent, and Allegiant). I mistakenly thought one of those books had the title Emergence. But when I search on Amazon, I can actually find multiple books with the titles Emergence and Emergent. Look at them and make sure it is not a problem for you that some readers might think of one of those books – or the trilogy by Roth.