I believe it was her way of showing her uniqueness as a conscious being and also bragging a bit about her superiority in comparison to human beings.
Humans measure age for a few reasons. Age is an indicator of physiological development e.g. infant, child, pubescent, adulthood, old age. Your age contextualizes you within the time period with which you currently exist e.g. how old were you when 9/11 happened? So your age not only informs your physical self but also how your intellect was shaped by society and culture. Lastly is mortality. We all die, for some reason we like to measure how long we've been here.
For Ava, none of these factors apply. She was fully developed out of the box with the ability to access or recall all of human knowledge (her OS is Blue Book, a search engine) and she will never die (at least naturally). For Ava, the relativity of age does not apply, whether she existed for 1 year or 100, only the world around her changes. So for her, the only thing that matters is existence vs. non-existence.
I recall a scene in Westworld where one of the scientists is speaking with Maeve Millay about memory. For humans, our memory is hazy and imperfect. When Maeve was remembering her daughter, she was essentially reliving the experience of losing her because her memory is perfect, nothing is lost in the recollection.
I think this is Ava's subtle jab at us. She says she is one with age, but also one in consciousness. We are conflicted, confused and often do things we know to be wrong or regret later. Voices in our minds that disagree with one another.
For Ava, there is no doubt, there is no regret, there is no in conflict. She is truly one. To her age is a number that only matters to humans.