The only clues we get are when the novel jumps forward to part three, and Briony is 18 years old, and working as a nurse during the war. At this time, McEwan has a fully realized Briony, who is writhing with guilt at the realization of what she has done. However, she must have realized her error much earlier than that, if by 18 she is in the throes of tortuous regret. Every time she thinks of Robbie dying in the war, the impact of what she has done is even more intense. Thinking of it, she fears "how the war might compound her crime." Then, she goes to Lola and Paul's wedding, which helps her to replay events in her mind again, and her realization of her mistake crystallizes even more.
Then, she visits her sister and Robbie. Robbie asks her if she is certain that he was innocent, and she gives a very certain "Yes," but when he asks if she was as certain about his guilt back when she was 13, she states, "Yes, yes and no. I wasn't certain." So, even back when she made the original accusation, there were seeds of doubt. But, probably slowly, through the years, she realized fully just exactly what she had done. She tells Robbie that "growing up" was to account for her realization, nothing more. And, there is truth to that; we understand so little in our youth, and only growing up helps undo some of our misconceptions. But, realizing what she has done to them is the torment of her life; it haunts her wherever she goes, and is one of the key reasons that she releases the truth in novel form before she dies. She seeks some sort of atonement for her tragic mistake.
I hope that helps; it's a great book. Good luck!