I think “Once upon a time” is a splendid beginning. I use it sometimes to get me going if I’m writing something of the fantasy persuasion. If another genre, it’s my habit to say “So I guess it starts with…” which was a suggestion from someone or other on the NaNoWriMo forum last year. It never fails to encourage more words to appear on the page.
I’ve decided to begin writing a story on here. No planning. No pre-determined length. No vicious internal editor. Just putting (digital) words on the (virtual) page for you to read at your leisure. Why? Because I’m a person who loves beginnings, even when they all pile up on one another to drown me in the excitement of their newness. Look for this to start in the new year.