Gurgeh seems to be in his mid-60's. This is confirmed when he realises that Contact have been keeping the Azadian Empire secret since it's initial discovery 74(ish) years ago. When he finally learns that he was played as a patsy for Special Circumstance, he then asks whether he was bred by SC for the specific purpose of becoming the top game player of all time, playing Azad and defeating the Empire.
'And when did you first get that sniff of contact?' Gurgeh said, turning to the drone. 'How long have you been sitting on this?'
The drone hesitated. 'Not long,' it said eventually. 'Seventy-three years.'
'You people certainly don't rush into things, do you?'
'Only when we've no choice,' the drone agreed.
and
'All my life,' Gurgeh said quietly, looking past the drone to the dull, dead landscape outside the tall windows. 'Sixty years… and how long has the Culture known about the Empire?'
Suffice to say, the drone's response is emphatic that they didn't.