They become full mages three years after their initiation convocation (the one where they received their full mage implants, and their ships), that they had when they were 21 years old.
Hence, they can become full mages at 24, assuming normal progress. The initiation class of 2258 was a special case though. Being in hiding has stunted the progress of most of the class, because they, certainly unlike Galen, and unlike even Kane, Finian and Gwynne, have not had as much real world experience during their probationary period. Remember, Kane, Finian and Gwynne were called cloister mages. They've spent much of the time in hiding, and have less real world experience than Galen.
By the time we see Galen in A Call to Arms, he's been a full mage for at least 5 years (given Elric's appraisal of Galen's progress just prior to Elric's death).