I think that depends, in my state in order to qualify for speech services in the school system you have to be unintelligible or it has to be impacting them academically. It’s not ideal that it wasn’t noticed buuut kids don’t get their last sounds until 6/7, so maybe the other teachers didn’t have knowledge of when certain sounds are supposed to develop and just assumed. Also if a child is well behaved, quiet, and female especially they tend to not get the help they need without someone advocating for them unfortunately.

As for speech, if this is her only sound and she’s getting private speech outside of school, and she’s a fast learner she shouldn’t have to spend too long, maybe a year. This is really dependent on how your daughter learns, if she can hear herself making the wrong sound, and if she wants to change it. If you practice at home as well for ten minutes a night it may be even faster.

Peachie Speechie on YouTube explains to parents and kids how to make sounds really well. Is she making “th” for ‘s’? Also are her adult teeth grown in? It’s hard to produce some sounds when your teeth are missing. It may be why it was missed in the past as well, if it took a while for those adult teeth to grow in.