The phrase "dawning awareness" means slowly starting to realize or understand something. It is like a light beginning to shine and reveal something previously unknown or not fully understood. Full definition
For some, Katrina brought a terrible, dawning awareness of how dangerous it can be to be poor in America, to not have resources or access to the very services that could save the lives of your loved ones. (animalsheltering.org)
As she tracks Scout's dawning awareness of the realities of life in the South, Witherspoon's wonderfully effective reading captures both character and tone in an insightful performance of Lee's controversial novel. (booklistonline.com)
And the dawning awareness of just how much business value can be unlocked by a skilful analyst has made employers more likely to pay competitively. (canadianbusiness.com)