Yes, you definitely can decide when you want to send your child in for playgroups. I didn't start my son on any formal playgroup until he was 18 months and even then it was only 1x a week. When he turned 2.5yo, we made it 3x per week. Playgroups are pretty informal and are, essentially, "play" groups (with some being more structured than others). It's just that some centres who offer playgroups are more popular than others, hence the wait lists, but with HK being such a transient place, places can often free up partly through the term.
Nurseries often accept kids once they turn 2. Same situation as playgroups: the more popular (not necessarily better) nurseries might have wait lists, but you can always put your name down, if you want to.
No need to over-stress. As far as I know, here in HK, a child does not HAVE to be in school until P1, although many parents would want to have their child/ren in kindy at the latest.
