Does anyone know roughly when the first GS class will be? Likely spring/summer 2022?
That's a pretty good and realistic guess.
Current pool candidates are likely to begin in March and April. From there it will depend on how long their training takes, so non-pooled pilots could expect start dates into probably late May, into June. Of course, that depends on how bad Omicron gets. There is no mention of conducting more layoffs, but new hires may be delayed if it turns out the South Africans are wrong, and this variant is both more transmissible and deadly than Delta was/is. Naturally, that may mean the likes of Encore get busier as people change international travel plans to domestic plans.
Best bet is to get the resume in now and hope for a call. If there is one thing this pandemic has reinforced, it's that if you want to be an airline pilot, get in early because a seniority number is better than gold.