Allopurinol starts working on the first day. Gout is simply a slow disease… you can have it for a long time before you notice it and curing it is likewise very slow regardless of whether you do it with allopurinol or anything else.
Be sure to double-check your uric acid test results though. You can get allopurinol-induced attacks even though the dose is insufficient which would be a real shame.
I’m not a big fan of prolonged use of indomethacin-type drugs. These drugs are invaluable if you get hit by a serious attack (indeed you could probably take more than three per day if it was really severe but check with your doc first). The thing is, there are side-effects which can develop over time, some of which are deadly. People often think nothing of it since doctors hand out such drugs routinely and you can get them directly from a pharmacist without checking with a doctor first. But this class of drugs actually kills lots of people every year. They aren’t very dangerous as such but they are frequently abused.
In particular if you’re going to take one pill every day, I would recommend looking at different drugs within this class. The one my rheuma gave me when I started a drug similar to allopurinol is banned in some countries so I’m not going to recommend it but there are many alternatives which are supposed to have fewer side-effects than indomethacin. With any of these drugs, if you take it every day you want to get very regular blood tests which can detect some of the painless side-effects early.
And be sure to check your blood pressure a couple of times when you feel especially “high”.
Also see if there’s any way you could adjust your diet in order to allow you to go off this statin for a while. If that could allow you to use colchicine, this could potentially end up being a life saver.