FTB buying a shared ownership house – timeline after local search and enquiries?

Hi everyone,
Me and my partner are first-time buyers and we’re in the process of buying a shared ownership house. I’m just trying to get a realistic idea of the timeline from here.
Current position:
Our mortgage offer has been issued.
Our solicitor has now received the final local authority search and said they’ll be sending enquiries this week.
The EA has already been asking us when we’re looking to complete we know the sellers are keen to move fairly quickly.
Our solicitor was quite vague and said it’s difficult to suggest dates but “July/August” for completion.
We’re hoping to complete in around 3–4 weeks if everything goes smoothly, ideally by the week commencing 20th July.
For anyone who’s bought a shared ownership property:
How long did it take from enquiries being raised to exchange?
Were the enquiries mostly routine?
How quickly did you complete after exchange?
Does a late July completion sound realistic, or am I being too optimistic?
I know every transaction is different, but it’d be really helpful to hear other people’s experiences and timelines.
Thanks!