Having been in a national recruiting role with Deloitte for 10+ years before recently retiring, I can verify that we had a “December class” every year, for as long as I can remember. I had many discussions with recruits weighing offers from other consulting firms, including some of the other “Big Four”. (I can’t speak for my Audit/Advisory colleagues - they ran a completely separate effort).
Recruiting for those classes took place in the fall, so you son would need to wait until his “extras” semester for recruiting. The good news is that this process has become earlier and earlier over the years. When campus visits were in November, with offers going out in Jan/Feb. this would be a challenge. Full-time recruiting is now a compressed September-October process (at least pre-pandemic).