So doing some research for my new story idea and found a PDF from the LAFD about Recruit Training Academy Overview from September 2017.
And I'm now pretty convinced I've found the class/group that Buck would have been a part of...
So if we go with the pilot episode that aired on Jan 3, 2018, as that is the week that episode happens in canon, then Buck has been a probationary firefighter for what four months. Okay, then you go back four months from Jan 2018, and you get September 2017. In September 2017, there's a class graduating from the academy to probation. (Note, there's about 4/5 classes each calendar year)
Now, season 2 episode 1 aired on September 23, 2018, well the class that Buck would be apart of would have their probationary year end on September 17, 2018
To summarise, this means Buck's academy class would be called 2016-4 (this is because of the fiscal year of 2016/17), it would start on May 1, 2017, he would graduate on September 14, 2017, and his probation would end on September 17, 2018.
