First sentences range from formulated literary manifestations to frenzied statements born of a muse's dictation. They can make or break a manuscript, whether the consequences are worthy or not. Nobody has perfect knowledge on how to write their "hook", as some call it. An assortment of factors contribute to success or failure on page one.
The first sentence can have a huge impact on your first draft, especially if you are a discovery writer. A bit of character, setting, or plot can be a seed destined to become a sprawling tree. Plant one of those seeds in the ground and set your frenzied fingers on your keyboard. Emotion and wonder are the gardener's till. When you strike the earth, you'll either unearth a brilliant story or hit stone. If you're plagued by the latter, wait for something else, try a plot a few acres over. Seeing a girl weilding a claymore in some funny little cloud as you break the earth may very well thrust you into a journey through medieval Scotland via the mind of a tenacious young heroine. The rest will fall into place if the wind is right.
An outliner's lead must be a cornerstone, despite the nonsensical architectural notion. Every word should serve a purpose. Don't waste words. What you do with your first sentence is up to you. Is the setting what will get my readers to turn the page? Or is it Marcus, the selfless paladin from a merchant town in the hills? Whatever it is, exploit it. Make your readers feel familiar in your world, but with an inkling of enthusiasm toward touring "the strange". Having your story fleshed out within your imagination can be a great help in reasoning what will need to be included.
My process for first sentences is rather plain. Occasionally I'll have an idea that must be written forthwith, riddled with passion. These tend to fall flat, too powerful for me to contain. It takes a weightlifter to pick them up. Usually I'll simply start with a name, have them do something, and the rest is history. Character is my go-to. From there some aspect of plot is likely to push me into a grand adventure or a serene setting may set my eyes to twinkling.
Revisions are rarely kind to first sentences. If they aren't completely replaced by your final draft they've likely been reworded and reworked until they hardly resemble their influencial ancestor. That isn't to say the original is a waste of time to write; the effects of it are huge. However, once you've reached the end of a tale the beginning never feels quite the same as it did before. New life springs into a polished first sentence, driving the direction of numerous subsequent edits.
The first sentence to one Mary Robinette Kowal novel was omitted in its first printing. Some may find that problem a small one, yet that is far from the truth. Without a book's first sentence it has lost much more than a handful of words thrown onto paper. It has been rid of its soul.