It is not discrimination if they require an ATP for their operations (they do since they type everybody up front) and the government requires age 23 for the ATP. There are many government jobs (law enforcement and military officer) which have explicit or implicit age minimums.
As for your application...personally I would be impressed at someone your age with those qualifications. I would send in an app and explain your situation in the cover letter. That leaves them the option of:
A. Waiting until you turn 23 to interview you OR
B. Interviewing you now, and delaying your class date until after your b-day.
I can't imagine it annoying them...just don't whine about age discrimination. Nobody would ever take that seriously when talking about young people...it only works on the other end of the spectrum.