Huge congratulations!
You can apply for the Adoption Order after 10 weeks of placement at the earliest. Many adopters choose to delay applying, for various reasons, so that will make the time to celebration hearing longer, obviously.
Once you have applied, the court will set a date for the child's LA to supply all the paperwork, which in our LA is usually about 6 weeks after they have received the application. The court also sets a date for an initial hearing, which in our LA is usually about 4 weeks later again. So on the whole, another 10 weeks from when you applied. At least. It can be significantly longer, e.g. if the courts are very busy. In our case we 'lost' a month due to the court legal advisor sending back our application claiming we had made a mistake, when in fact we hadn't. It took a month to clear that up and get it back to the court.
At the initial hearing, if there are no problems, the AO can be granted and a date is set for the celebration hearing. In our case the celebration hearing was about 3 weeks later and our SW said that this is standard. However if the adoption is contested, it can be months and months from the initial hearing until the AO is granted. For example: At the initial hearing, BM requests leave to contest. Gets given time to put case together, and new hearing date set. At next hearing, BM gets more time to put case together. New date set. At this new hearing BM's request for leave to contest is denied. BM appeals this decision. New hearing is scheduled to hear this appeal. Appeal is rejected and new date is scheduled to hear application for AO, and finally AO is granted and date for celebration hearing set - maybe 4 or 5 months after initial hearing.
So that would add up as:
10 weeks of placement until you can apply for AO
10 weeks from application to initial hearing
3 weeks from granting of AO to celebration hearing
adding up to 23 weeks from today, or over 5 months.
-> as absolutely minimum timescale.