Have you heard about how Bono of U2 writes a song?
It starts with a choon. Maybe a guitar riff. A drum beat. A melody. A hook. The rest of the band bring their ideas to the party.
Then Bono improvises words as sounds to fit the music. At first his words aren't even sentences and aren't even in English. They are snippets, phrases, bits of foreign languages, made up words, baby speak.
http://www.atu2.com/news/the-songwriters-u2-where-craft-ends-and-spirit-begins.html
Then edit, edit, edit. Move ideas around, play with sounds, swap, mix and match.
Repeat until done.
Don't worry that the first few attempts are rubbish. That's perfectly okay. Withhold judgement until much much later. All too often we fall out of love with something because it doesn't look good at the beginning.
Take these hands
Teach them what to carry
Take these hands
Don't make a fist
Take this mouth
So quick to criticize
Take this mouth
Give it a kiss
The other way to start is to find the sentence that defines the entire work. "
In a hole in the ground there lived a hobbit." "It was the best of times, it was the worst of times".
A final thought - and this is a Once theory and not U2, so is almost certainly not as good! I like to start and end a story with bookends. I nearly always have a scene or an idea at the beginning of a story (or even a piece of non fiction) which is then echoed at the end. A bit like the Hobbit or LOTR starting and ending in the Shire.
That way the reader knows that the story has ended, and it is right that it should end where it does. It also provides a framework for a character arc because the main character should be both recognisably the same and also noticeably changed by the process.
Thinking about the bookends often helps me to frame the first and last words, or at the least the first and last scenes/ ideas.
Sometimes these bookends come to me before I start. At other times they appear magically during the writing process. Purely a personal thing but it works for me.