Every thing happens at what my Teacher calls 'God's Hour.' I did not know till I was nearly 30, and then my re-awakening happened by reading a book. Knowing what I know now, I feel that even this is an act of Grace.
An awareness of Destiny is generally a conscious thing. We are perhaps all vaguely aware on an unconscious level. Still, each Soul wants a different experience and as such destiny, in the sense of what we are meant to do, may be covered up. Prayer and meditation expedites this process.
There is another kind of destiny called Fate or Prarabda Karma. Here we are experiencing the results past and present of our causes and effects. Before we can become conscious and move on, they have to be burnt out. Again, this requires Grace from God or the presence of a Spiritual Master, a God-realised Soul.
I figured you meant knowing life's purpose. They are all related. Some people find it even without conscious awareness, as they came specifically to fulfill that cause. Still, no matter how we look at it, it's mostly, not totally, all Cause and Effect, Action and Reactions in the end. It is a process of growth or experiences that all Souls must travel on their way back to the Godhead. Some are further along the way.