I know he said he joined at 13, I'm pretty sure he said that he had 5 years of training before he did the become-a-full-templar ritual. So he's at least 18 when he goes to Kinloch tower. Nothing specific is said about what age he actually did go to Kinloch or how long he was there before being transferred to Kirkwall. He must have been pretty new during the mage origin to have never attended a harrowing before, and he had to be at Kinloch at least a year, since the events of DA:O take a year I believe. So my guess is that by the time DA:I starts, which is in 9:41 (right?), Cullen is about 30.
Just to clarify - are we sure that the Warden mage's harrowing was his first? We know that he hadn't seen abominations up till that point, but I assumed it was because the apprentices who were actually approved for a Harrowing probably passed, though possibly ungracefully. If I recall correctly, codex entries in DAO explain that Irving/the higher ups pay close attention to negative personality traits to weed out potential problems early - Jowan wasn't going to be allowed to undergo the Harrowing for that reason. The two gossiping mage girls that are in the room when you wake up from your Harrowing also say that Cullen said your Harrowing was "the quickest and cleanest he'd ever seen" and that your Warden was "very talented", so I figure he'd been through a few already without incident.
He does says in DAI that he's "attended a few" Harrowings when asked about what Templar duties involve, so I assume they just weren't especially frequent occurrences. But yeah, I agree he's probably in his early thirties at least. Sure wish we had more concrete info about it, but I can see why they'd want to leave that to headcanon too, haha.