It's like that scene in Spongebob. You spend hours slaving over an essay to find that all you have written down is "The" in antiquated font. Don't worry. The writing process is not that painful, but getting started is half the battle. Writing that golden first sentence will put you on track for an exceptional college application essay. Every subsequent piece of your essay stems from that sentence, so, make it memorable and impactful; first impressions matter.
There are several approaches. Your ultimate goal is to grab the reader by the collar and have the words compel him/her to keep reading. You have to put yourself in the shoes of an adcom who has been reading essays for hours. What would catch your eye? What would pique your interest? For example, here is how I began my Common App essay:
"Sweet tones of roasted cardamom pods flirt with the minty fragrance of freshly stained henna adorning my mother's palms."
You can see that the sentence captivates the reader's sense of smell and vision. It draws the reader in, making him/her more inclined to read into the words that I spent months (literally) perfecting. How many people do you think begin their essay talking about cardamom and henna? Not many.
You may, however, wish to commence what could be the most important essay of your life with a quote. Don't. The idea of using a quote is so overdone and stale that it would likely put your adcom to sleep before he/she even gets into the meat of what you want to convey. There are some instances, however, in which a quote may summarize one of your experiences or reflect one of your personal goals/ideals. It is difficult to pull off, but may be worth it. I often refer to Malala Yousafzai's famous line: "One child, one teacher, one book, and one pen can change the world." It's clear, impactful, and, most importantly, not overused. (Tip: Anything about shooting for the stars or missing 100% of the shots you don't take is probably not the best thing to start an essay with.)
A solid way to begin any piece of writing is a short, declarative (and often dramatic or perplexing) statement. "I change my name each time I place an order at Starbucks," an opening sentence from a Stanford admissions essay, epitomizes such a statement. It's condensed, yet interesting. You can see that it is not flowery or extravagant. Simplicity can be beautiful when writing. While this starkly contrasts my melody of an opening line, it serves the same purpose - to intrigue. The reader wonders why the student changes his/her name with every order, and what the deeper implications of such a statement may be. You simply want to know more. This simple sentence, only twelve words, immediately grabs the reader's attention and draws him/her into the rest of the essay. This is a win.
Your opening statement(s) do not have to be overly dramatic, academic, flowery, etc. They simply have to make the adcom want to read more. That's your mission. The approach you take is not as important as how you execute it. So, go forth and write the best opening line you can think of! Or, at least write something, scrap it, and write again. Remember, the first few words are often the most difficult. So, take your time (but not too much time).