Cullen looks far older than he acts in DA:O, but many characters in DA:O looked old to me. For instance, Alistair looked 28-33 to me but based on everything else we know (plus the way he acts), Alistair was probably 20-22 during the Blight.
During the male mage origin, Cullen states that "this is all new to me" after expressing his concerns about what an abomination might be or might look like. We could read that as him having an uneventful, peace experience as a templar but it doesn't seem all that plausible.
I suspect that Cullen had been recently promoted to the full duties of a templar shortly before the warden takes her/his Harrowing and I'd also guess that was Cullen's first Harrowing.
My guess is that Cullen is close in age to the Warden and/or Hawke. I'll guess anything between 20-25 during the DA:O origin story, but the fact that Meredith is willing to quickly promote Cullen to Knight-Captain in DA2 makes me wonder if he's at the older end of that range.
For my headcanon (and upcoming fic if I find time to write) unless I have reason to reconsider I'm giving him a birthday in 9:06 in the middle of the
Seventh Month of Solis, just before the Funalis Annum holiday. So, that would make him 23-24 during the Blight, 27-28 when Hawke is made Champion, and 30-31 when Anders blows up the Chantry. It sort of feels right to me, sort of.