The question of whether or not Damian, in the New Age (New 52) was conceived and born before Bruce became Batman or during his first year as Batman has been mused upon by comic book fans and chronologists at conventions, comic shops, and on message boards for the past year. DC has yet to address this in its new comic continuity, so until they do, everything surmised is pure speculation. So far, it is my belief that Bruce trained in his early pre-Batman years with Ra's Al Ghul, met Talia around that time, knocked her up, and had little Damian. Many argue that Damian's growth was artificially sped up by League of Assassins scientists, meaning that even if he was conceived as little as five years ago, he could still look like a ten-year-old in 2011 or 2012. This doesn't really sit well with me, for a laundry list of reasons that I won't bother delving into at this juncture. (Ask me and I'll tell you why if you are truly interested!)
I've chosen a few selections from message boards and internet forums that seem to grasp the New 52 Damian conundrum with an open and enlightened mind. Note that a few of these selections quote Scott Snyder. I have yet to confirm any of the Snyder quotes and don't know where these commentators got them from. However, the quotes directly from writers and artists like James Tynion and Greg Capullo, we can take as gospel. Here are just handful of the many, many posts I've scrutinized on the web that deal not only with Damian's age and conception, but the ages of the other Bat Family members as well:
--Anonymous on the Warner Bros/DC Comics message boards/forum (Sept. 13, 2011):
"Scott Snyder has stated that Damian was conceived while Batman was training, which is in his first year. [...] He says that Bruce will float around 33-35 [years of age] in character personality. Snyder [also says] ... [Batman has been active for] roughly 10 years, roughly [33-35 years old].
--Theozilla on the CBR forum/message boards (Sept. 9, 2011):
"[Scott] Synder basically says Bruce is around 33 years old and that gives him about 12 years of activity, which all the Robins can be squeezed into."
--James Tynion IV (Batman Vol. 2 writer!) says in a CBR interview with Jeffrey Renaud (Feb. 29, 2012):
"The back-up [story in Batman Vol. 2 #8], "The Fall of the House of Wayne," is set around 33 years ago, in Bruce's infancy."
--Greg Capullo (Batman Vol. 2 artist!) on the CBR forums (Sept. 24, 2011):
"The [editor-in-chief, Bob Harras,] said [in regard for how old to make the characters look when drawing them in Batman Vol. 2 #1], ages 30 [for Bruce], 19 [—later changed to 21 for Dick], 16 [for Tim], and 10 [for Damian]."
--Grim on ComicVine message boards/forum (Nov. 22, 2011):
"The one thing you can guess for sure is that all the Robins were only Robin for 2-4 years. Dick is only in his 20s, as is Barb[ara Gordon]."
--TheLuckyOne on CBR message boards (Sept. 4, 2011):
"The ways around [continuity issues regarding Damian’s conception] ... are to either say Damian was artificially aged [quickly], or change Son of the Demon to say Bruce wasn't Batman yet when he and Talia were together."
--SeoulCanuck on CBR message boards (July 21, 2011):
"Doesn't it make more sense for Bruce to have met and trysted with Talia during his "roaming the world, learning from masters" phase, long before he ever put on the cowl? That would mean Talia hadn't drugged and raped him, of course, but it's a lot easier to accept a teenage mistake than artificially aging what would be a three-year-old into a tween's body, isn't it? Why wouldn't Talia have just made him into an adult, if she could clone and indoctrinate the clone that well? It means jettisoning a little bit of Bat-history, but DCnU certainly doesn't seem reluctant to mess with the history of their other icon."
--Vitruvian on CBR message boards (July 21, 2011):
"[The New 52] is better [off] by far to have Bruce and Talia get together while Bruce was roaming the world training himself for his war on crime; maybe even include some of the Nolan movie elements of some of that training coming from the League of Shadows, if not direct tutelage by the Demon's Head himself (or maybe that stays good, too)."