Once the physical cab is there, it could go live within days, or 6 months. There may still be work to do on tie cables, power and fibre - any of which might already be done, or might be outstanding (and having problems).
3 months was a rule-of-thumb, but I have the impression that BT are reducing that a little now.
However, there is someone on here whose cabinet has been there for over a year, unpowered, IIRC.
Hey, walked down and checked the box today, put my ear to the vents on the back of the box and heard a whirring noise, is that what you mean? There definitely was noise coming from it. Hope that means something!