I find getting off to a a good start on a story is invaluable. Those first few words show me the scene, sometimes a little bit of the main character, but it is enough for me to get going with the longer piece. I also find I have got to have a title to work to but am more than happy to change this later should I need to do so. I see the title as a kind of "peg" to hang my story on and if I need to change "pegs" then so be it.
Do your characters find getting off to a good start vital for them to have a chance at achieving overall success in whatever it is they are doing? Frodo Baggins certainly did in The Lord of The Rings! That headstart as he began his quest to get rid of the Ring of Power was crucial. So how do your characters define what a good start is for them and how do they achieve it?