While I do not know exactly what kind of essay you intend to write or what points you might be making, it is clear that you have to capture your audience's attention for any effective essay. And, if you have to (or just want to) write that introduction in Squeaky's voice, you will automatically capture your readers' attention because that is just what Squeaky does with everyone she meets.
Your best bet to recreate Squeaky's "voice" is to say something sassy, which is exactly what she does. To do that, perhaps you can model one of the tones she uses in this story and adapt it to whatever you want to say.
One thing Squeaky does not lack is self-confidence; in fact, she often seems cocky and arrogant, as in the following statement:
So as far as everyone’s concerned, I’m the fastest and that goes for Gretchen, too, who has put out the tale that she is going to win the first-place medal this year. Ridiculous. In the second place, she’s got short legs. In the third place, she’s got freckles. In the first place, no one can beat me and that’s all there is to it.
While it is certainly pretty arrogant to make such a claim, we are not offended because we know Squeaky is not just talk; she works hard and is therefore just demonstrating her supreme confidence. In the next example, Squeaky is a little more informative. She tells us what she likes and how she likes it--and what she does if she does not like it:
So then I think I’ll just walk straight on through them or even over them if necessary. But as they get to me, they slow down. I’m ready to fight, cause like I said I don’t feature a whole lot of chit-chat, I much prefer to just knock you down right from the jump and save everybody a lotta precious time.
Finally we have the insult. Squeaky, in her righteous indignation, will not allow anyone to give her or her brother, Raymond, any grief. She dishes the insults here:
“You got anything to say to my brother, you say it to me, Mary Louise Williams of Raggedy Town, Baltimore.... That’s right, Fatso. And the next word out of anybody and I’ll be their mother too.”
Raking one of these as your guide, speak your words in her voice. If you are writing a persuasive essay, she might tell us what other people believe, but her is what she believes and why. If you are writing an informative essay, she might treat us (readers) as if this information is something everyone should already know. In any case, if you can capture her tone, you will be able to say anything you want.